# Does conservation of energy make black holes impossible?

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I was musing today about black holes, and came across what seems to be a contradictory fact about black holes. If any matter were to actually fall into a black hole, it seems like it would need to gain infinite energy.

This is seen by considering an object close to the event horizon of a black hole. If we consider escape velocity for a particle at the event horizon, it has an escape velocity of the speed of light. The energy required to achieve this escape velocity would therefore be infinite. As we approach the event horizon, it seems like we should be able, then, to define an arbitrarily small distance across which the particle gains an arbitrary amount of energy.

As the object approaches arbitrarily close to the event horizon, it seems like its relativistic mass would therefore grow arbitrarily high, resulting in a corresponding increase in the gravity of the black hole, which seems impossible.

If we extrapolate back to the formation of the black hole, it then seems like it should be impossible for any particles to fall into the black hole, even as it forms. Instead, mass should be distributed in a probability cloud whose density asymptotically approaches zero at the event horizon of the black hole. New particles could then enter this cloud of incredibly dense (but not black hole dense) matter, where they would be captured rather than falling past the event horizon, within which there would be a vacuum.

If this were true, there would be no black holes, only hollow spheres of radiation and matter which externally look like black holes, since their gravity would be great enough that particles entering the sphere would exit at an incredibly slow rate. Interestingly, such spheres wouldn't suffer from the apparent information paradox that black holes do.

That or I'm missing an obvious explanation for why that's all wrong, which seems more likely because I'm neither a physicist nor an astronomer. What's the critical flaw in this argument?

Let's reformulate your argument as follows (using idealized assumptions for simplicity):

1. An object some distance away from the black hole has potential energy equal to the kinetic energy it would have at the event horizon.

2. This is the same amount of energy that would be required to pull the object from the event horizon back to its original position (and velocity).

3. We would need to accelerate the object to the escape velocity to return it to its position.

4. Since the escape velocity is greater than c, it would take an infinite amount of energy to return it to its position.

The incorrect point is 3. We can pull an object out of a gravitational field slowly by exerting a force on it the whole way. We would only need to accelerate it to the escape velocity if we wanted it to escape "on its own", i.e. without us exerting a force to keep pushing it away from the black hole.

EDIT: I'm less sure of my answer after doing some back-of-the-envelope calculations. It would be helpful for a real expert to weigh in. I'll leave my answer here anyway.

For simplicity, let's consider a Schwarzschild black hole, so that the spacetime is spherically symmetric and static. In particular, the Schwarzschild time $t$ coordinate gives a direction in which the geometry 'stays the same' (a Killing vector field), and its inner product with the orbital four-velocity $u$ is conserved: $$epsilon = -g(u,partial_t) = left(1-frac{2M}{r} ight)frac{mathrm{d}t}{mathrm{d} au} ext{,}$$ where $au$ is the proper time of the orbiting particle. One can think of this as the specific (per-mass) energy, including mass-energy: a particle escaping to infinity that becomes asymptotically at rest with respect to stationary observers would have $epsilon = 1$.

If we consider escape velocity for a particle at the event horizon, it has an escape velocity of the speed of light. The energy required to achieve this escape velocity would therefore be infinite.

The energy as measured by whom? Imagine a family of stationary observers everywhere surrounding the black hole, or at least along an infalling particle's trajectory. Those observers measure the speed and energy of the particle as it falls past them. As the particle nears the horizon, they will report speeds arbitrarily close to the speed of light and arbitrarily high energies.

But to a far-away stationary observer, those observers near the horizon are experiencing increasingly divergent gravitational time dilation, and the orbital energy of the particle stays constant. Flinging a particle of mass $m$ into the black hole will increase the mass of the black hole by $mepsilon$.

What's the critical flaw in this argument?

All energy gravitates, so I would say the main flaw is forgetting to add the gravitational potential energy of the particle to the mass of the black hole as well. Or better put, you should be concerned with the orbital energy, not just its mass+kinetic parts ('relativistic mass').

In this situation, you have a well-defined conserved orbital energy. If you insist on measuring the Lorentz factor according to close-by stationary observers, then yes, it diverges to $+infty$, but then you would have to admit a gravitational potential energy term that diverges to $-infty$, because their sum must resolve to be the orbital energy.

## Celestia Forums

There are also theories about the fact that M31 Milky way are close enough that in a few billion years the gravity created by the to SMBH's(Supermassive black holes) of both galaxys will eventually suck eachother together thus fusing the galaxys together and destroying great amounts of both galaxys. The two SMBH's will form one great UMBH(Ultramassive Black hole) and if our solar system is lucky we will be jetisoned out of the fused galaxy, or we will sucked into the UMBH. That's all I know now

### Re: Supermassive Black Holes

Post #4 by Tanketai » 22.09.2005, 03:26

Well, I for one wouldn't put it that way. Sucking energy suggests an active search for energy (like a vacuum cleaner) black holes deform space in a way that energy (as light or matter) just happen to move towards it.

Quoting the Hitchhiker's Guide to the Galaxy:

"In Relativity, Matter tells Space how to curve, and Space tells Matter how to move."

And I also wouldn't put it that way: a black hole could be considered as a point, as it dimensions wouldn't be really relevant, only it's mass. A galaxy, however. if you're talking about planets, nebulas and stars, then a galaxy is a really, really big thing (and not point-like).

If you consider the fact that galaxies are made of matter (no, seriously, wait me finish) then they would not be destroyed by the collision. So what if a few stars (really few of them would really colide) get blown up? They would turn into new nebulas, that would condensate into new stars. Some of the galaxy's matter could, of course, be flung into deep space, thus torning it apart, but not really destroying it.

And I would not put that that way, either. If you make a quick search through the posts on this forum, you'll probably find all of these things you said (wrote) explained in a much more detailed way. As we say over here: C?? n??o t?? com essa bola toda.

Heh, I like the Hitchhikers guide.

Anyways. I'm glad you pointed out my errors, which infeact were quite obvious, but still with the collision damage thing, when the stars and such collide, yes they will become nebulas but, they will most like be absorbed by the immense power of the UMBH.

Post #6 by WildMoon » 22.09.2005, 22:46

Pi does not equal 3.14159265, it equals "yum!"

A world without Monty Python, gnomes, news crews that make a big deal out of a celebrity breathing, Star Trek, & Coca-Cola? That is impossible! IMPOSSIBLE!

Post #7 by Tanketai » 22.09.2005, 23:00

No, they did not compress it. they've only used the very end of the 'trilogy' to wrap it up (the earth mark 2 part, except for the 'so long and thank you' bowls)

But as for the galaxy being 'eaten' by the black hole, that's not being destroyed as well, if you're thinking about matter. Just remember Hawking's evaporating black holes. (it's like when a kid eats a coin: if it came in, it has got to come out)

Post #8 by WildMoon » 22.09.2005, 23:20

Still, would be better if they would do 5 movies for the books.

Black holes pull matter towards them then when the matter reaches the black hole itself the matter is crushed into an infinitly dense space. When the black hole eventually evaporates, radiation is released.

Pi does not equal 3.14159265, it equals "yum!"

A world without Monty Python, gnomes, news crews that make a big deal out of a celebrity breathing, Star Trek, & Coca-Cola? That is impossible! IMPOSSIBLE!

Post #10 by WildMoon » 23.09.2005, 00:29

Pi does not equal 3.14159265, it equals "yum!"

A world without Monty Python, gnomes, news crews that make a big deal out of a celebrity breathing, Star Trek, & Coca-Cola? That is impossible! IMPOSSIBLE!

Post #12 by WildMoon » 23.09.2005, 00:49

hmm, also if energy is compressed enough it'll turn into an matter and antimatter pair. But the matter and antimatter would instantly cansel each other out creating pure energy. But what if this happened to energy pull into the black hole, could the matter and antimatter pair instantly be converted into radiation before canceling each other out?

Speaking of antimatter, when the big bang occured radiation was constantly being converted to matter-antimatter pairs which would then cancel each other out and form pure radiation yet somehow there was enough matter left over the form our universe today. but what happened to the antimatter? At some point I think that something made the matter and antimatter separate when the matter-antimatter pairs were created. But what happpened to the antimatter? Could it be that the dark matter observed in our universe is really clumps of antimatter?

Pi does not equal 3.14159265, it equals "yum!"

A world without Monty Python, gnomes, news crews that make a big deal out of a celebrity breathing, Star Trek, & Coca-Cola? That is impossible! IMPOSSIBLE!

Post #13 by Malenfant » 23.09.2005, 03:26

Don't think it is actually. IIRC black holes don't actually remove anything from the universe (well, beyond putting it behind an event horizon) and when they evaporate they should release the same amount of energy that corresponds to the mass that they have absorbed over their entire evaporation lifetime.

um, no. IIRC black holes lose energy because virtual matter/antimatter pairs are created naturally in space anyway. But when the pair straddles the event horizon of a BH, one goes into the hole and the other goes into the universe outside, and that takes energy out of the hole somehow (I'm fuzzy on the details, it's been a while since I read about this).

No, because we'd be able to detect radiation emitted from it as it interacted with normal matter around it (eg interstellar gas). Plus, there's no reason why we wouldn't be able to detect it if it was antimatter. If there is anything made of antimatter in the universe, we haven't seen it yet.

As for what happened to the antimatter, it got annihilated at the start. We're made of matter because there was a bit more matter than antimatter at the beginning. The antimatter annihilated with all the matter that it could and was depleted, leaving behind the excess matter.

Ive got a few questions hopefully someone can answer.

1) If you were to look at a black hole, would it appear flat. If so, what would you see when looking at it side on?

Assuming you are not talking about the event horzon, aren't non-rotating black holes the size of a point?

Assuming you are not talking about the event horzon, aren't non-rotating black holes the size of a point?

Well I understand they can increase in mass, but in dimensions? How?
Or are you talking about the event horizon?

Black hole mass/energy can be measured by means of its gravitational field, charge and rotation rate. The size and shape of the event horizon (EH) is then inferred by means of GR theory.

## Ask Ethan: When Do Black Holes Become Unstable?

The simulated decay of a black hole not only results in the emission of radiation, but the decay of . [+] the central orbiting mass that keeps most objects stable. Black holes are not static objects, but rather change over time.

There are quite a few ways to make the black holes we know about in the Universe, from core-collapse supernovae to merging neutron stars to the direct collapse of tremendous amounts of matter. On the smallest end, we know of black holes that may be merely 2.5-to-3 times the mass of our Sun, while on the largest end, supermassive ones in excess of 10 billion solar masses reside at the centers of galaxies. But is that it? And how stable are black holes of different masses? That's what Nyccolas Emanuel wants to know, as he asks:

Is there a critical size for black hole stability? [A] 10 12 kg [black hole] is already stable for a couple of billion years. However, a [black hole] in the range of 10 5 kg, could explode in a second, thus, definitely not stable. I guess there is a critical mass for a [black hole] where the flow of gained matter will equal to the Hawking evaporation?

There's a lot going on here, so let's unpack it all.

Black holes will devour whatever matter they encounter. Although this is a great way for black holes . [+] to grow, Hawking radiation also ensures that black holes will lose mass. Deriving when one defeats the other is not a trivial task.

X-ray: NASA/CXC/UNH/D.Lin et al, Optical: CFHT, Illustration: NASA/CXC/M.Weiss

The first thing to start with is the stability of a black hole itself. For any other object in the Universe, astrophysical or otherwise, there are forces that hold it together against whatever the Universe might do to try and tear it apart. A hydrogen atom is a tenuously held-together structure a single ultraviolet photon can destroy it by ionizing its electron. An atomic nucleus needs a much higher-energy particle to blast it apart, like a cosmic ray, an accelerated proton, or a gamma-ray photon.

But for larger structures, like planets, stars or even galaxies, the gravitational forces holding them together are enormous. Normally, it takes either a runaway fusion reaction or an incredibly strong, external gravitational pull — such as from a passing star, black hole, or galaxy — to tear such a megastructure apart.

NGC 3561A and NGC 3561B have collided and produced huge stellar tails, plumes and even possibly . [+] "ejecta" that are condensing to make tiny "new" galaxies. Hot young stars glow blue where rejuvenated star formation is taking place. Forces, such as those between galaxies, can rip stars, planets, or even entire galaxies apart. Black holes, however, will remain.

Adam Block/Mount Lemmon SkyCenter/University of Arizona

For black holes, however, something is fundamentally different. Rather than their mass being distributed over a volume, it's compressed down into a singularity. For a non-rotating black hole, that's just a single, zero-dimensional point. (For rotating ones, it's not much better: an infinitely-thin, one-dimensional ring.)

Furthermore, all of the mass-and-energy-containing contents of a black hole are contained within an event horizon. Black holes are the only objects in the Universe that contain an event horizon: a boundary where, if you slip within it, it's impossible to escape. No acceleration, and hence no force, no matter how strong, will ever be able to pull matter, mass, or energy from inside the event horizon outside to the Universe beyond.

Artist's impression of the active galactic nucleus. The supermassive black hole at the center of the . [+] accretion disk sends a narrow high-energy jet of matter into space, perpendicular to the disc. A blazar about 4 billion light years away is the origin of many of the highest-energy cosmic rays and neutrinos. Only matter from outside the black hole can leave the black hole matter from inside the event horizon can ever escape.

DESY, Science Communication Lab

This might imply that black holes, once you form one via any means possible, can only grow, and never be destroyed. In fact, they do grow, and relentlessly at that. We observe all sorts of phenomena in the Universe, such as:

• quasars,
• blazars,
• active galactic nuclei,
• microquasars,
• stars orbiting large masses that emit no light of any type,
• and flaring, X-ray and radio emissions from galactic centers,

that are all thought to be driven by black holes. By inferring their masses, we can thereby know the physical sizes of their event horizons. Anything that collides with it, crosses over into it, or even grazes it will inevitably fall inside. And then, by the conservation of energy, it must inevitably increase the black hole's mass.

An illustration of an active black hole, one that accretes matter and accelerates a portion of it . [+] outwards in two perpendicular jets, is an outstanding descriptor of how quasars work. The matter that falls into a black hole, of any variety, will be responsible for additional growth in both mass and size for the black hole.

This is a process that, on average, is happening for every black hole in the Universe known today. Material from other stars, from cosmic dust, from interstellar matter, gas clouds, or even the radiation and neutrinos left over from the Big Bang can all contribute. Intervening dark matter will collide with the black hole, increasing its mass as well. All told, black holes grow depending on the matter-and-energy density surrounding them the monster at the center of our Milky Way grows at a rate of about one solar mass every 3,000 years the black hole at the center of the Sombrero galaxy grows at a rate of one solar mass every two decades.

The larger and heavier your black hole is, on average, the faster it grows, dependent on the other material it encounters. As time goes on, the rate-of-growth will drop, but with a Universe that's only about 13.8 billion years old, they continue to grow prodigiously.

If event horizons are real, then a star falling into a central black hole would simply be devoured, . [+] leaving no trace of the encounter behind. This process, of black holes growing because matter collides with their event horizons, cannot be prevented.

On the other hand, black holes aren't just growing over time there's also a process by which they evaporate: Hawking radiation. This was the topic of last week's Ask Ethan, and is due to the fact that space is severely curved close to the event horizon of a black hole, but flatter farther away. If you are an observer a great distance away, you'll see a non-negligible amount of radiation being emitted from the curved region near the event horizon, owing to the fact that the quantum vacuum has different properties in differently-curved regions of space.

The net result is that black holes wind up emitting thermal, blackbody radiation (mostly in the form of photons) in all directions around it, over a volume of space that mostly encapsulates approximately ten Schwarzschild radii of the location of the black hole. And, perhaps counterintuitively, the less massive your black hole is, the faster it evaporates.

The event horizon of a black hole is a spherical or spheroidal region from which nothing, not even . [+] light, can escape. But outside the event horizon, the black hole is predicted to emit radiation. Hawking's 1974 work was the first to demonstrate this, and it was arguably his greatest scientific achievement.

NASA Dana Berry, SkyWorks Digital, Inc.

Hawking radiation is an incredibly slow process, where a black hole the mass of our Sun would take 10 64 years to evaporate the one at the Milky Way's center would require 10 87 years, and the most massive ones in the Universe could take up to 10 100 years . In general a simple formula you can use to calculate the evaporation time for a black hole is to take the timescale for our Sun and multiply it by:

(Mass of the black hole/Mass of the Sun) 3 ,

which means that a black hole of the Earth's mass would survive 10 47 years one the mass of the Great Pyramid at Giza (

6 million tons) would remain for about a thousand years one the mass of the Empire State building would last for about a month one the mass of an average human would last just under a picosecond. As your mass decreases, you evaporate more quickly.

The decay of a black hole, via Hawking radiation, should produce observable signatures of photons . [+] for most of its life. At the very end-stages, though, the rate of evaporation and the energies of the Hawking radiation means there are explicit predictions for the particles and antiparticles that would be unique. A human-mass black hole would evaporate in about a mere picosecond.

For all that we know, the Universe could contain black holes of an extraordinarily wide range of masses. If it were born with light ones — anything below about a billion tons — those would all have evaporated by the present day. There is no evidence of black holes that are heavier than that until you get to the ones created by neutron star-neutron star mergers, which begin to arise at about 2.5 solar masses in theory. Above that, X-ray studies point to the existence of black holes in the range of

10-20 solar masses LIGO has shown us black holes ranging from 8 up to approximately 62 solar masses and astronomy studies reveal the supermassive black holes that are found throughout the Universe.

There's a wide range of black holes that we know of, but also a wide range of studies that rule out black holes composing a majority of the dark matter over a huge variety of regimes.

Constraints on dark matter from Primordial Black Holes. There is an overwhelming set of pieces of . [+] evidence that indicate there is not a large population of black holes created in the early Universe that comprise our dark matter.

Fig. 1 from Fabio Capela, Maxim Pshirkov and Peter Tinyakov (2013), via http://arxiv.org/pdf/1301.4984v3.pdf

Today, all the black holes that actually, physically exist are gaining matter at a far greater rate than Hawking radiation is causing them to lose mass. For a solar-mass black hole, it loses about 10 -28 Joules of energy every second. Considering that:

• even a single photon from the Cosmic Microwave Background has about a million times that energy,
• there are about 411 such photons (left over from the Big Bang) per cubic centimeter of space,
• and they move at the speed of light, meaning approximately 10 trillion photons-per-second collide with every square-centimeter of area an object takes up,

even an isolated black hole in the depths of intergalactic space would have to wait until the Universe was around 10 20 years old — more than a billion times its current age — before the rate of black hole growth drops below the rate of Hawking radiation.

The core of galaxy NGC 4261, like the core of a great many galaxies, show signs of a supermassive . [+] black hole in both infrared and X-ray observations. As matter falls into it, the black hole continues to grow.

But let's play the game. Assuming you lived in intergalactic space, away from all normal matter and dark matter, away from all cosmic rays and stellar radiation and neutrinos, and only had the photons left over from the Big Bang to contend with. How big would your black hole need to be so that the rate of Hawking radiation (evaporation) and the rate of photon absorption by your black hole (growth) balanced each other?

The answer comes out to around 10 23 kg, or approximately the mass of the planet Mercury. If it were a black hole, Mercury would be approximately a half-a-millimeter in diameter, and would radiate approximately 100 trillion times as quickly as a solar mass black hole. That's the mass, in the Universe today, that it would take for a black hole to absorb as much Cosmic Microwave Background radiation as it would emit in Hawking radiation.

As a black hole shrinks in mass and radius, the Hawking radiation emanating from it becomes greater . [+] and greater in temperature and power. However, by time the Hawking radiation rate exceeds the growth rate, there will be no stars left burning in our cosmos.

For a realistic black hole, you cannot isolate it from the remaining matter in the Universe. Black holes, even if they get ejected from galaxies, still fly through the intergalactic medium, encountering cosmic rays, starlight, neutrinos, dark matter, and all sorts of other particles, both massive and massless. The cosmic microwave background is unavoidable no matter where you go. If you're a black hole, you're constantly absorbing matter-and-energy, and growing in both mass and size as a result. Yes, you radiate energy away, too, in the form of Hawking radiation, but for all black holes that actually exist in our Universe, it will take at least 100 quintillion years for the rate-of-growth to drop below the rate of radiation, and much, much longer for them to finally evaporate away.

Black holes will eventually become unstable and disappear into nothing but radiation, but unless we create a very low-mass one, somehow, nothing else in the Universe will be around to witness them when they go.

## Do Black Holes Destroy Energy?

I am a student at school, and we are learning about types of energy's. Going off what my teacher has said, (Something like the Law of The Conservation of Energy) according to that, energy cannot be destroyed only transferred or transformed. Since light has no mass what happens to the light when it enters a black hole? What happens to the light energy when it enters the black hole? I assume it wouldn't transfer the energy since the black hole can't absorb it's mass to get bigger. so where does it go? Does it get destroyed? (Some information or reasoning for thinking this in the question might be wrong so please correct me if it is).

Energy can be converted to mass, and vice-versa. This is how nuclear power works: when a heavy nucleus breaks up into smaller parts, the sum of the parts is less massive than the original nucleus. That lost mass is actually contained in the kinetic energy of the particles, or in photons depending on the type of decay.

We don't really know what happens inside of a black hole, conceptually it's just a dimensionless point in space that has mass, charge, and angular momentum, but when you add energy to it it's the same as adding mass. That is to say, the black hole gets bigger.

We don’t really know what happens inside of a black hole, conceptually it’s just a dimensionless point in space

Many people by “black hole”, understand the area inside the event horizon.

That's good to note- I didn't know that energy could be converted into mass if I am being real honest. Thanks for letting me know. I also got information from some other sources and it said light had no mass so I assumed there was no way to make it into mass.

does that not mean that it has relativistic mass, not a "resting" mass? e=mc² would equal 0 if there was truly no mass.

The law of conservation of energy is extended by recognising that energy and mass can be converted into each other. Or to put it another way, mass is a form of energy.

So energy that crosses the event horizon of a black hole simply adds to the black hole's mass.

Short answer, No. Long answer. no..well maybe. Avoiding the math for a simpler explanation, let's just pretend blackholes are a party guest. And food at the party is energy. Conceptually we have a decent grasp on what happens when every other guest eats. They chew the food, they digest it, the usable stuff is added to their mass and energy stores, the unusable converted to waste and discarded. Blackholes don't seem to play by the same rules but they do follow those rules in theory just on a difficult to measure scale. Now many theories swirl around blackholes and until we are all interstellar, some answers can only be seen as the favored theories not solid answers.

All that to say when we look at blackholes, it's eating the food, not bothering to take breaks and despite it's size it's mass is far higher than anything other single celestial body. Energy and Mass are inter-related, to keep it simple. Converting Mass to energy is getting tons of bang for your buck in most cases. Like Hydrogen bombs to nuclear fusion. Minus the whole could kill everything, it's a good time for those who get to use that energy. However Blackholes take in both mass and energy, they eat light, and spit out energy when it eats large amounts, like a messy eater. Back to our party and our disruptive Blackhole in attendance. We see him or her eating everything but rarely do we see it expel anything. And if it eats enough we believe it grows in mass. But if it eats a lot rapidly, we see huge streams of electromagnetic energy being shot out. I won't claim to know the full science or anything beyond that, and sadly most can't tell you with confidence, if that stream of energy is indicative of messy eating or rapid gravitational forces forcing the food that can't get to mouth fast enough to be shot out. But energy is being taken in and energy is coming out. And even blackholes decay. Despite how weird it is, it is operating within the rules of math and physics, best we know. My best answer is change the question, are blackholes turning energy into mass? Which best we can tell, yea kinda. So why did I say maybe, cause no one can quantify for sure that all the mass (potentially turned to energy) and energy is accounted for. So speaking out of the realm of what's known, maybe cause whose to say for sure the full energy of an eaten star is accounted for in energy shots, and mass being added.

## Black Holes at the Extreme

Physicists see very easily that charged black holes reach an extremal limit. When they combine Einstein’s gravity equations and the equations of electromagnetism, they calculate that a black hole’s charge, Q, can never surpass its mass, M, when both are converted into the same fundamental units. Together, the black hole’s mass and charge determine its size — the radius of the event horizon. Meanwhile, the black hole’s charge also creates a second, “inner” horizon, hidden behind the event horizon. As Q increases, the black hole’s inner horizon expands while the event horizon contracts until, at Q = M, the two horizons coincide.

If Q increased further, the radius of the event horizon would become a complex number (involving the square root of a negative number), rather than a real one. This is unphysical. So, according to a simple mashup of James Clerk Maxwell’s 19th-century theory of electromagnetism and Einsteinian gravity, Q = M must be the limit.

When a black hole hits this point, a simple option for further decay would be to split into two smaller black holes. Yet in order for such splitting to happen, the laws of conservation of energy and conservation of charge require that one of the daughter objects must end up with more charge than mass. This, according to Einstein-Maxwell, is impossible.

But there might be a way for extremal black holes to split in two after all, as Nima Arkani-Hamed, Lubos Motl, Alberto Nicolis and Cumrun Vafa pointed out in 2006. They noted that the combined equations of Einstein and Maxwell don’t work well for small, strongly curved black holes. At smaller scales, additional details related to the quantum mechanical properties of gravity become more important. These details contribute corrections to the Einstein-Maxwell equations, changing the prediction of the extremal limit. The four physicists showed that the smaller the black hole, the more important the corrections become, causing the extremal limit to move farther and farther away from Q = M.

The researchers also pointed out that if the corrections have the right sign — positive rather than negative — then small black holes can pack more charge than mass. For them, Q > M, which is exactly what’s needed for big extremal black holes to decay.

If this is the case, then not only can black holes decay, but Arkani-Hamed, Motl, Nicolis and Vafa showed that another fact about nature also follows: Gravity must be the weakest force. An object’s charge, Q, is its sensitivity to any force other than gravity. Its mass, M, is its sensitivity to gravity. So Q > M means gravity is the weaker of the two.

From their assumption that black holes ought to be able to decay, the four physicists made a more sweeping conjecture that gravity must be the weakest force in any viable universe. In other words, objects with Q > M will always exist, for any kind of charge Q, whether the objects are particles like electrons (which, indeed, have far more electric charge than mass) or small black holes.

This “weak gravity conjecture” has become hugely influential, lending support to a number of other ideas about quantum gravity. But Arkani-Hamed, Motl, Nicolis and Vafa didn’t prove that Q > M, or that extremal black holes can decay. The quantum gravity corrections to the extremal limit might be negative, in which case small black holes can carry even less charge per unit mass than large ones. Extremal black holes wouldn’t decay, and the weak gravity conjecture wouldn’t hold.

This all meant that researchers needed to figure out what the sign of the quantum gravity corrections actually is.

## Contents

Black holes are astrophysical objects of interest primarily because of their immense gravitational attraction. A black hole forms when enough matter and/or energy is compressed into a volume small enough that the escape velocity is greater than the speed of light. Nothing can travel that fast, so nothing within a distance, defined by the mass of the black hole, can move beyond that distance. The boundary of this sphere is the event horizon an observer outside it cannot observe, become aware of, or be affected by events within the event horizon. This region is the black hole's boundary, in effect.

It is unknown what exactly happens to the mass inside a black hole. It is possible that a gravitational singularity forms at the center - a point of zero size and infinite density. Our current understandings of physics can be used to predict what may happen in the region of the event horizon. In 1974, British physicist Stephen Hawking used quantum field theory in curved spacetime to show that in theory, the force of gravity at the event horizon was strong enough to cause energy to "leak" into the wider universe within a tiny distance of the event horizon. In effect this energy acted as if the black hole itself was slowly evaporating (although it actually came from outside it). [4] [ citation needed ]

Hawking's insight was based on a phenomenon of quantum physics known as virtual particles and their behaviour near the event horizon. Even in empty space, subatomic "virtual" particles and antiparticles come briefly into existence, then mutually annihilate and vanish again. Close to a black hole, this manifests as pairs of photons. [2] One of these photons might be pulled beyond the event horizon, leaving the other to escape into the wider universe. Careful analysis showed that if this happened, quantum effects would cause a "partner wave" carrying negative energy to be created and also pass into the black hole, reducing the black hole's total mass, or energy. [2] In effect, to an observer it would appear as if the gravitational force had somehow allowed the black hole's energy to be reduced and the energy of the wider universe to be increased. Hence black holes must gradually lose energy and evaporate over time. [2] Considering the thermal properties of black holes, and conservation laws affecting this process, Hawking calculated that the visible outcome would be a very low level of exact black-body radiation - electromagnetic radiation produced as if emitted by a black body with a temperature inversely proportional to the mass of the black hole. [2]

Physical insight into the process may be gained by imagining that particle–antiparticle radiation is emitted from just beyond the event horizon. This radiation does not come directly from the black hole itself, but rather is a result of virtual particles being "boosted" by the black hole's gravitation into becoming real particles. [ citation needed ] If this theoretical particle–antiparticle pair was produced by the black hole's gravitational energy, the escape of one of the particles would reduce the mass of the black hole. [5]

An alternative view of the process is that vacuum fluctuations cause a particle–antiparticle pair to appear close to the event horizon of a black hole. One of the pair falls into the black hole while the other escapes. In order to preserve total energy, the particle that fell into the black hole must have had a negative energy (with respect to an observer far away from the black hole). This causes the black hole to lose mass, and, to an outside observer, it would appear that the black hole has just emitted a particle. In another model, the process is a quantum tunnelling effect, whereby particle–antiparticle pairs will form from the vacuum, and one will tunnel outside the event horizon. [ citation needed ]

An important difference between the black hole radiation as computed by Hawking and thermal radiation emitted from a black body is that the latter is statistical in nature, and only its average satisfies what is known as Planck's law of black-body radiation, while the former fits the data better. Thus, thermal radiation contains information about the body that emitted it, while Hawking radiation seems to contain no such information, and depends only on the mass, angular momentum, and charge of the black hole (the no-hair theorem). This leads to the black hole information paradox.

However, according to the conjectured gauge-gravity duality (also known as the AdS/CFT correspondence), black holes in certain cases (and perhaps in general) are equivalent to solutions of quantum field theory at a non-zero temperature. This means that no information loss is expected in black holes (since the theory permits no such loss) and the radiation emitted by a black hole is probably the usual thermal radiation. If this is correct, then Hawking's original calculation should be corrected, though it is not known how (see below).

A black hole of one solar mass ( M ) has a temperature of only 60 nanokelvins (60 billionths of a kelvin) in fact, such a black hole would absorb far more cosmic microwave background radiation than it emits. A black hole of 4.5 × 10 22 kg (about the mass of the Moon, or about 133 μm across) would be in equilibrium at 2.7 K, absorbing as much radiation as it emits. [ citation needed ]

Hawking's discovery followed a visit to Moscow in 1973, where the Soviet scientists Yakov Zel'dovich and Alexei Starobinsky convinced him that rotating black holes ought to create and emit particles. When Hawking did the calculation, he found to his surprise that even non-rotating black holes produce radiation. [6] In 1972, Jacob Bekenstein conjectured that the black holes should have an entropy, [7] where by the same year, he proposed no hair theorems. Bekenstein's discovery and results are commended by Stephen Hawking which also led him to think about radiation due to this formalism.

Hawking radiation is required by the Unruh effect and the equivalence principle applied to black hole horizons. Close to the event horizon of a black hole, a local observer must accelerate to keep from falling in. An accelerating observer sees a thermal bath of particles that pop out of the local acceleration horizon, turn around, and free-fall back in. The condition of local thermal equilibrium implies that the consistent extension of this local thermal bath has a finite temperature at infinity, which implies that some of these particles emitted by the horizon are not reabsorbed and become outgoing Hawking radiation. [8]

The black hole is the background spacetime for a quantum field theory.

The field theory is defined by a local path integral, so if the boundary conditions at the horizon are determined, the state of the field outside will be specified. To find the appropriate boundary conditions, consider a stationary observer just outside the horizon at position

The local metric to lowest order is

The horizon is not a special boundary, and objects can fall in. So the local observer should feel accelerated in ordinary Minkowski space by the principle of equivalence. The near-horizon observer must see the field excited at a local temperature

The gravitational redshift is given by the square root of the time component of the metric. So for the field theory state to consistently extend, there must be a thermal background everywhere with the local temperature redshift-matched to the near horizon temperature:

The inverse temperature redshifted to r′ at infinity is

and r is the near-horizon position, near 2M , so this is really:

So a field theory defined on a black hole background is in a thermal state whose temperature at infinity is:

This can be expressed in a cleaner way in terms of the surface gravity of the black hole this is the parameter that determines the acceleration of a near-horizon observer. In Planck units ( G = c = ħ = kB = 1 ), the temperature is

where κ is the surface gravity of the horizon (in units of lightspeed per Planck-time squared). So a black hole can only be in equilibrium with a gas of radiation at a finite temperature. Since radiation incident on the black hole is absorbed, the black hole must emit an equal amount to maintain detailed balance. The black hole acts as a perfect blackbody radiating at this temperature.

In SI units, the radiation from a Schwarzschild black hole is blackbody radiation with temperature

where ħ is the reduced Planck constant, c is the speed of light, kB is the Boltzmann constant, G is the gravitational constant, M is the solar mass, and M is the mass of the black hole.

From the black hole temperature, it is straightforward to calculate the black hole entropy. The change in entropy when a quantity of heat dQ is added is:

The heat energy that enters serves to increase the total mass, so:

The radius of a black hole is twice its mass in Planck units, so the entropy of a black hole is proportional to its surface area:

Assuming that a small black hole has zero entropy, the integration constant is zero. Forming a black hole is the most efficient way to compress mass into a region, and this entropy is also a bound on the information content of any sphere in space time. The form of the result strongly suggests that the physical description of a gravitating theory can be somehow encoded onto a bounding surface.

When particles escape, the black hole loses a small amount of its energy and therefore some of its mass (mass and energy are related by Einstein's equation E = mc 2 ). Consequently, an evaporating black hole will have a finite lifespan. By dimensional analysis, the life span of a black hole can be shown to scale as the cube of its initial mass, [9] [10] : 176–177 and Hawking estimated that any black hole formed in the early universe with a mass of less than approximately 10 15 g would have evaporated completely by the present day. [11]

In 1976, Don Page refined this estimate by calculating the power produced, and the time to evaporation, for a nonrotating, non-charged Schwarzschild black hole of mass M . [9] The time for the event horizon or entropy of a black hole to halve is known as the Page time. [12] The calculations are complicated by the fact that a black hole, being of finite size, is not a perfect black body the absorption cross section goes down in a complicated, spin-dependent manner as frequency decreases, especially when the wavelength becomes comparable to the size of the event horizon. Page concluded that primordial black holes could only survive to the present day if their initial mass were roughly 4 × 10 14 g or larger. Writing in 1976, Page using the understanding of neutrinos at the time erroneously worked on the assumption that neutrinos have no mass and that only two neutrino flavors exist, and therefore his results of black hole lifetimes do not match the modern results which take into account 3 flavors of neutrinos with nonzero masses. A 2008 calculation using the particle content of the Standard Model and the WMAP figure for the age of the universe yielded a mass bound of (5.00 ± 0.04) × 10 14 g . [13]

If black holes evaporate under Hawking radiation, a solar mass black hole will evaporate over 10 64 years which is vastly longer than the age of the universe. [14] A supermassive black hole with a mass of 10 11 (100 billion) M will evaporate in around 2 × 10 100 years . [15] Some monster black holes in the universe are predicted to continue to grow up to perhaps 10 14 M during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 10 106 years. [14]

The power emitted by a black hole in the form of Hawking radiation can easily be estimated for the simplest case of a nonrotating, non-charged Schwarzschild black hole of mass M . Combining the formulas for the Schwarzschild radius of the black hole, the Stefan–Boltzmann law of blackbody radiation, the above formula for the temperature of the radiation, and the formula for the surface area of a sphere (the black hole's event horizon), several equations can be derived.

The Hawking radiation temperature is: [3] [16] [17]

The Bekenstein–Hawking luminosity of a black hole, under the assumption of pure photon emission (i.e. that no other particles are emitted) and under the assumption that the horizon is the radiating surface is: [17] [16]

where P is the luminosity, i.e., the radiated power, ħ is the reduced Planck constant, c is the speed of light, G is the gravitational constant and M is the mass of the black hole. It is worth mentioning that the above formula has not yet been derived in the framework of semiclassical gravity.

The time that the black hole takes to dissipate is: [17] [16]

where M and V are the mass and (Schwarzschild) volume of the black hole. A black hole of one solar mass ( M = 2.0 × 10 30 kg ) takes more than 10 67 years to evaporate—much longer than the current age of the universe at 14 × 10 9 years . [18] But for a black hole of 10 11 kg , the evaporation time is 2.6 × 10 9 years . This is why some astronomers are searching for signs of exploding primordial black holes.

However, since the universe contains the cosmic microwave background radiation, in order for the black hole to dissipate, the black hole must have a temperature greater than that of the present-day blackbody radiation of the universe of 2.7 K. In 2020, Chou proposed a theory if a Pluto-mass rotating radiating primordial black hole, the Hawking radiation temperature will be 9.42 K, higher than 2.7 K CMB. [19] Other study suggest that M must be less than 0.8% of the mass of the Earth [20] – approximately the mass of the Moon.

Black hole evaporation has several significant consequences:

• Black hole evaporation produces a more consistent view of black hole thermodynamics by showing how black holes interact thermally with the rest of the universe.
• Unlike most objects, a black hole's temperature increases as it radiates away mass. The rate of temperature increase is exponential, with the most likely endpoint being the dissolution of the black hole in a violent burst of gamma rays. A complete description of this dissolution requires a model of quantum gravity, however, as it occurs when the black hole's mass approaches 1 Planck mass, when its radius will also approach two Planck lengths.
• The simplest models of black hole evaporation lead to the black hole information paradox. The information content of a black hole appears to be lost when it dissipates, as under these models the Hawking radiation is random (it has no relation to the original information). A number of solutions to this problem have been proposed, including suggestions that Hawking radiation is perturbed to contain the missing information, that the Hawking evaporation leaves some form of remnant particle containing the missing information, and that information is allowed to be lost under these conditions.

### Trans-Planckian problem Edit

The trans-Planckian problem is the issue that Hawking's original calculation includes quantum particles where the wavelength becomes shorter than the Planck length near the black hole's horizon. This is due to the peculiar behavior there, where time stops as measured from far away. A particle emitted from a black hole with a finite frequency, if traced back to the horizon, must have had an infinite frequency, and therefore a trans-Planckian wavelength.

The Unruh effect and the Hawking effect both talk about field modes in the superficially stationary spacetime that change frequency relative to other coordinates that are regular across the horizon. This is necessarily so, since to stay outside a horizon requires acceleration that constantly Doppler shifts the modes. [ citation needed ]

An outgoing photon of Hawking radiation, if the mode is traced back in time, has a frequency that diverges from that which it has at great distance, as it gets closer to the horizon, which requires the wavelength of the photon to "scrunch up" infinitely at the horizon of the black hole. In a maximally extended external Schwarzschild solution, that photon's frequency stays regular only if the mode is extended back into the past region where no observer can go. That region seems to be unobservable and is physically suspect, so Hawking used a black hole solution without a past region that forms at a finite time in the past. In that case, the source of all the outgoing photons can be identified: a microscopic point right at the moment that the black hole first formed.

The quantum fluctuations at that tiny point, in Hawking's original calculation, contain all the outgoing radiation. The modes that eventually contain the outgoing radiation at long times are redshifted by such a huge amount by their long sojourn next to the event horizon, that they start off as modes with a wavelength much shorter than the Planck length. Since the laws of physics at such short distances are unknown, some find Hawking's original calculation unconvincing. [21] [22] [23] [24]

The trans-Planckian problem is nowadays mostly considered a mathematical artifact of horizon calculations. The same effect occurs for regular matter falling onto a white hole solution. Matter that falls on the white hole accumulates on it, but has no future region into which it can go. Tracing the future of this matter, it is compressed onto the final singular endpoint of the white hole evolution, into a trans-Planckian region. The reason for these types of divergences is that modes that end at the horizon from the point of view of outside coordinates are singular in frequency there. The only way to determine what happens classically is to extend in some other coordinates that cross the horizon.

There exist alternative physical pictures that give the Hawking radiation in which the trans-Planckian problem is addressed. [ citation needed ] The key point is that similar trans-Planckian problems occur when the modes occupied with Unruh radiation are traced back in time. [8] In the Unruh effect, the magnitude of the temperature can be calculated from ordinary Minkowski field theory, and is not controversial.

### Large extra dimensions Edit

The formulae from the previous section are applicable only if the laws of gravity are approximately valid all the way down to the Planck scale. In particular, for black holes with masses below the Planck mass (

10 −8 kg ), they result in impossible lifetimes below the Planck time (

10 −43 s ). This is normally seen as an indication that the Planck mass is the lower limit on the mass of a black hole.

In a model with large extra dimensions (10 or 11), the values of Planck constants can be radically different, and the formulae for Hawking radiation have to be modified as well. In particular, the lifetime of a micro black hole with a radius below the scale of the extra dimensions is given by equation 9 in Cheung (2002) [25] and equations 25 and 26 in Carr (2005). [26]

where M is the low energy scale, which could be as low as a few TeV, and n is the number of large extra dimensions. This formula is now consistent with black holes as light as a few TeV, with lifetimes on the order of the "new Planck time"

### In loop quantum gravity Edit

A detailed study of the quantum geometry of a black hole event horizon has been made using loop quantum gravity. [27] [28] Loop-quantization reproduces the result for black hole entropy originally discovered by Bekenstein and Hawking. Further, it led to the computation of quantum gravity corrections to the entropy and radiation of black holes.

Based on the fluctuations of the horizon area, a quantum black hole exhibits deviations from the Hawking spectrum that would be observable were X-rays from Hawking radiation of evaporating primordial black holes to be observed. [29] The quantum effects are centered at a set of discrete and unblended frequencies highly pronounced on top of Hawking radiation spectrum. [30]

### Astronomical search Edit

In June 2008, NASA launched the Fermi space telescope, which is searching for the terminal gamma-ray flashes expected from evaporating primordial black holes.

### Heavy-ion collider physics Edit

In the event that speculative large extra dimension theories are correct, CERN's Large Hadron Collider may be able to create micro black holes and observe their evaporation. No such micro black hole has been observed at CERN. [31] [32] [33] [34]

### Experimental Edit

Under experimentally achievable conditions for gravitational systems this effect is too small to be observed directly. However, signals can be simulated in a laboratory experiment involving optical light pulses under conditions that are closely related to black hole Hawking radiation (see Analog models of gravity).

In September 2010 an experimental set-up created a laboratory "white hole event horizon" that the experimenters claimed was shown to radiate an optical analog to Hawking radiation. [35] However, the results remain unverified and debatable, [36] [37] and its status as a genuine confirmation remains in doubt. [38] Some scientists predict that Hawking radiation could be studied by analogy using sonic black holes, in which sound perturbations are analogous to light in a gravitational black hole and the flow of an approximately perfect fluid is analogous to gravity. [39] [40]

Other projects have been launched to look for this radiation within the framework of analog models of gravity.

## Black hole thermodynamics

In the 1800s scientists studying things like heat and the behavior of low density gases developed a theory known as thermodynamics. As the name suggests, this theory describes the dynamic behavior of heat (or more generally energy). The core of thermodynamics is embodied by its four basic laws.

The zeroth law states that if object A is in thermodynamic equilibrium with object B (meaning no net energy flows between them), and object C is in thermodynamic equilibrium with B, then A and C are in thermodynamic equilibrium with each other. Since objects in thermodynamic equilibrium have the same temperature, another way to state this law is that if A has the same temperature as B, and C has the same temperature as B, then A and C have the same temperature. When you put it that way it seems quite obvious, which is why it isn't known as the first law. The other laws were developed first, and as they were refined it became clear the zeroth law should be included as a physical property, not just an assumption.

The first law states that energy is conserved. Since heat is a form of energy, this means an object that is heating up must be getting energy from somewhere. Likewise, if an object is cooling down, the energy it loses must be gained by something else. Conservation of energy was known before thermodynamics, but this law recognized heat as a form of energy.

The second law is perhaps the most misunderstood law of thermodynamics. In its simplest form it can be summarized as "heat flows from hot objects to cold objects". But the law is more useful when it is expressed in terms of entropy. In this way it is stated as "the entropy of a system can never decrease." Many people interpret entropy as the level of disorder in a system, or the unusable part of a system. That would mean things must always become less useful over time, which is why evolution skeptics often claim it violates the second law of thermodynamics.

But entropy is really about the level of information you need to describe a system. An ordered system (say, marbles evenly spaced in a grid) is easy to describe because the objects have simple relations to each other. On the other hand, a disordered system (marbles randomly scattered) take more information to describe, because there isn't a simple pattern to them. So when the second law says that entropy can never decrease, it is say that the physical information of a system cannot decrease. In other words, information cannot be destroyed.

The third law basically states that at absolute zero an object is at its minimum possible entropy (often taken as zero). One consequence of this law is that you cannot cool an object to absolute zero.

In an earlier post I wrote about how classical black holes have "no hair", meaning that they are simply described by their mass, charge and rotation. Because of this, you could toss an object (with a great deal of entropy) into a black hole, and the entropy would simply go away. In other words, the entropy of the system would get smaller, which would violate the second law of thermodynamics. Another way of looking at it would be that the classical black hole has a temperature of absolute zero. This means you could take some hot mass and collapse it into a black hole, which would essentially be cooling an object to absolute zero, in violation of the third law of thermodynamics.

Of course, this ignores the effects of quantum mechanics. When we take quantum mechanics into account, black holes can emit light and other particles through a process known as Hawking radiation. Since a "quantum" black hole emits heat and light, it therefore has a temperature. This means black holes are subject to the laws of thermodynamics.

Integrating general relativity, quantum mechanics and thermodynamics into a comprehensive description of black holes is quite complicated, but the basic properties can be expressed as a fairly simple set of rules known as black hole thermodynamics. Essentially these are the laws of thermodynamics re-expressed in terms of properties of black holes.

The zeroth law states that a simple, non-rotating black hole has uniform gravity at its event horizon. This is kind of like saying that such a black hole is at thermal equlibrium.

The first law relates the mass, rotation and charge of a black hole to its entropy. The entropy of a black hole is then related to the surface area of its event horizon.

The second law again states that the entropy of a black hole system cannot decrease. One consequence of this is that when two black holes merge, the surface area of the merged event horizon must be greater than the surface areas of the original black holes.

The third law states that "extreme" black holes (those with a maximum possible rotation or charge) would have minimum entropy. This means that it would never be possible to form an extreme black hole. For example, it would never be possible to spin a black hole so fast that it would break apart.

The advantage of black hole thermodynamics is that provides a way to get a handle on the complex interactions black holes can have. Thermodynamic black holes have not just mass, charge and rotation, but also temperature and entropy. The rules first devised to describe the heating and cooling of simple gases also seems to apply to black holes.

But there are things we still don't understand about black hole thermodynamics. I'll talk about those next time.

## Is there a size limit to Black Holes?

Can black holes keep growing and growing indefinitely? Or at some point do they become unstable?

Also, let’s say (although very unlikely) that a black hole consumed an entire galaxy a long time ago, making it very big. But ever since then nothing has entered it. Would it eventually disappear (after a really long time) due to evaporation from Hawking Radiation?

One more question. Via E=MC^2 there is somewhat of an interchangeability or equivalence between energy and matter. Let’s say that you picked and object of mass M and threw it into a black hole. The black hole’s mass would increase by M. Now let’s say that instead of throwing object M into the black hole, you figure out how much energy E is equivalent to mass M via the above formula and then shoot lasers into the black hole of energy E. Would the black hole’s mass still increase by M by doing this since nothing can escape a black hole, not even light? If so, does that mean that black holes at the center of galaxies like ours are growing not only by sucking up matter, but also by absorbing light from all of the stars in our galaxy?

### #2 Sandy Swede

And the answer is . . . 50 billion solar masses.

### #3 rekokich

See the link regarding the upper limit to size

Yes, black holes would absorb laser light, and their mass should increase in accord with E = mc^2

In fact there are some very reasonable hypotheses that the very earliest supermassive black holes, formed during or immediately after the inflation phase of the Universe - in the radiation era, before matter became dominant - were formed entirely from radiation

### #4 BillP

FWIW, Quasars seem to have a black hole upper mass limit of 3 billion Suns.

However, we then have the anomaly of Quasar TON 618, which is estimated to have a back hole mass of 66 billion Sol masses! Although the measurement can always be off since the measures were indirect. Direct measures of Quasar Holm 15A confirm it is 40 billion Sol masses while indirect measures of it suggested much larger.

Edited by BillP, 15 February 2021 - 03:04 PM.

### #5 rekokich

The 2004 study you quote discusses supermassive black holes (SMBH) in the local universe at redshifts less than 2.1. Later studies by Kurt et al. (2007) and Jiang et al. (2007, 2010) with redshifts up to 5 show a much wider SMBH range, and the presence of much larger SMBHs in the early Universe. For example, at redshift z = 2, SMBH mass varies between 100 million and 10 billion solar. Also, their plot shows that SMBHs formed in the early Universe are about 40 times larger than the ones formed in recent epochs. At redshift z = 5 the maximum SMBH mass appears to be around 40 billion solar.

As you mention, TON 618 at redshift z = 2.219 is anomalous. It appears to have an SMBH of 66 billion solar masses. It is most likely a result of one or more SMBH mergers. The finding inspired theoretical cosmologists to speculate on the existence of SLABs, or stupendously large black holes with masses above 100 billion solar.

### #6 SnortEverything

In Schwarzschild cosmology it is proposed the observable universe is a black hole if the Hubble radius were equal to its Schwarzschild radius. The numbers are close but many would consider it a coincidence of lesser importance than say that of the large number coincidences. However, if that were the case, and our universe were in a black hole, it would appear we are pretty stable. As for the hypothetical point in which a black hole become unstable, have come to think a hypothetical instability may not result in a collapse/crunch but more of a 'pop' - a pressure release within the universal gradient that iterates and seeds the information for another cycle. This limit could be beyond that of the Planck density. Beyond that density violates the uncertainty principle for spacetime itself. I don't know how that could happen so just throwing it out there that maybe it could be from interactions with a tachyonic field interacting/colliding with our universe, flooding ours with negative mass.

However, if we were to picture an infinitely inflating universal black hole in geometric terms, there is still a larger number of terminations in the enclosed volume than the number of terminations on the surface. Thus only a certain amount of information­ energy remains expressed locally. Visually, can think of a plasma ball toy wherein the center has plasma discharges fluctuating and arcing to the glass orb around it. So, while two particles may disentangle/decohere, the information always has a path to inform the whole.

The problem with Hawking radiation is that to resolve the information paradox it was (pre 2004) thought by Hawking and those firmly in the relativity camp that quantum coherence is lost during evaporation. This would mean QM would not apply to black hole interactions. Furthermore, Hawking argued that once the loss of coherence is permitted in evaporation, it then would apply to all processes involving the planck scale. The world would behave as though it were a noisy environment with continual loss of coherence. One of the basic principles of QM is the evolution of pure states to pure states. The loss of coherence would break this fundamental principle. The issue is that there is no known way to destroy coherence without at the same time violating energy conservation by heating the world.

As for the last question, we would need a unified theory to understand more as to what is happening to that absorbed light. GR only goes so far as it describes a singularity forming from black hole gravity. One (very) hypothetical idea in loop quantum gravity is that at the singularity is a planck star. So the information is reposited and perhaps even deposited as a white hole.

In your example, that central galactic black hole is in isolation. Other smbh are also participants. The m-sigma relation shows correlation between black hole accretion rate and host galaxy star formation rate. This has led to the idea of "agn feedback". Extragalactic astronomers study star formation rate all day and night but I've been told studying this in active galaxies is extremely challenging to the point where skeptics believe that we don't really have reliable data to go off of. In active galaxies with quasars, the quasars screw up everything when measuring. You can't use traditional techniques of spatial resolution to measure black hole mass. You can't see the stars cause the quasar is too bright. You can't trust the data from gas cause it's being blown around by radiation pressure. You can hardly see the galaxy when put in high redshift. Measuring reliable masses seems very difficult with those observational challenges. However, there is a Chinese research group that began a reverberation mapping campaign a few years ago. They take up to 75-100% of the time on WIRO, OAGH, ANU, CAHA, LAMOST and YNAO telescopes.

## A short history of black holes

The story of how black holes (one illustrated) came to be accepted in science is a tale worth recounting.

Vchal/Istock/Getty Images Plus

Black holes have been sucking up scientific attention from the very beginning. They were hinted at as early as the 1780s. Albert Einstein predicted them in his general theory of relativity. But they didn’t get the name we know today until the 1960s.

#### Explainer: What are black holes?

Black holes were once thought to be only a mathematical curiosity. They were bizarre beasts that squashed gobs of matter into infinitely dense abysses. But bit by bit, astronomers tallied up evidence for black holes’ existence. They puzzled over where these behemoths live and how they gulp down matter. They questioned what the existence of black holes means for other physics theories.

For more than a decade, a team of researchers has been engrossed in an ambitious effort to snap a picture of a black hole for the very first time. Now, they’ve done it. What better time to think back to black holes’ origins and the journey so far?

### Power Words

American Association for the Advancement of Science (or AAAS) Formed in 1848, it was the first permanent organization formed to promote the development of science and engineering at the national level and to represent the interests of all its disciplines. It is now the world’s largest such society. Despite its name, membership in it is open to anyone who believes “that science, technology, engineering, and mathematics can help solve many of the challenges the world faces today.” Its members live in 91 nations. Based in Washington, D.C., it publishes a host of peer-reviewed journals — most notably Science.

archive (adj. archival) To collect and store materials, including sounds, videos, data and objects, so that they can be found and used when they are needed. The term is also for the process of collecting and storing such things. People who perform this task are known as archivists.

astronomy The area of science that deals with celestial objects, space and the physical universe. People who work in this field are called astronomers.

behemoth A term for anything that is amazingly big. The term comes from a monstrous animal described in the Bible’s book of Job.

black hole A region of space having a gravitational field so intense that no matter or radiation (including light) can escape.

data Facts and/or statistics collected together for analysis but not necessarily organized in a way that gives them meaning. For digital information (the type stored by computers), those data typically are numbers stored in a binary code, portrayed as strings of zeros and ones.

equation In mathematics, the statement that two quantities are equal. In geometry, equations are often used to determine the shape of a curve or surface.

evaporate To turn from liquid into vapor.

event horizon An imaginary sphere that surrounds a black hole. The more massive the black hole, the bigger the sphere. Anything that happens inside the event horizon is invisible, because gravity is so strong that under normal circumstances even light can’t escape. But according to some theories of physics, in certain situations small amounts of radiation can escape.

field An area of study, as in: Her field of research was biology. Also a term to describe a real-world environment in which some research is conducted, such as at sea, in a forest, on a mountaintop or on a city street. It is the opposite of an artificial setting, such as a research laboratory. (in physics) A region in space where certain physical effects operate, such as magnetism (created by a magnetic field), gravity (by a gravitational field), mass (by a Higgs field) or electricity (by an electrical field).

galaxy A massive group of stars bound together by gravity. Galaxies, which each typically include between 10 million and 100 trillion stars, also include clouds of gas, dust and the remnants of exploded stars.

gravity The force that attracts anything with mass, or bulk, toward any other thing with mass. The more mass that something has, the greater its gravity.

Hawking radiation The particles emitted from the event horizon on the outer edges of a black hole. Energy can be converted into a pair of particles. If that happens very close to outer edge of a black hole, one of those particles can tunnel out and become detected — providing the only direct physical clue to the black hole’s presence. These emissions are called Hawking radiation for Stephen Hawking, the famous British physicist who came up with the idea that black holes can emit particles.

haze Fine liquid or solid particles scattered through the atmosphere that make it hard to see. Haze can be caused by harmful substances such as air pollutants or by water vapor.

information (as opposed to data) Facts provided or trends learned about something or someone, often as a result of studying data.

information paradox (in physics) A problem created by two conflicting ideas about how black holes work and how the universe works. Black holes eventually disappear, and presumably, the information they contain about what’s in them also disappears. But this disappearance breaks a law of quantum mechanics, which says that information is never “lost” to the universe.

laser A device that generates an intense beam of coherent light of a single color. Lasers are used in drilling and cutting, alignment and guidance, in data storage and in surgery.

light-year The distance light travels in one year, about 9.48 trillion kilometers (almost 6 trillion miles). To get some idea of this length, imagine a rope long enough to wrap around the Earth. It would be a little over 40,000 kilometers (24,900 miles) long. Lay it out straight. Now lay another 236 million more that are the same length, end-to-end, right after the first. The total distance they now span would equal one light-year.

LIGO (short for Laser Interferometer Gravitational wave Observatory) A system of two detectors, separated at a great geographical distance, that are used to register the presence of passing gravitational waves.

mass A number that shows how much an object resists speeding up and slowing down — basically a measure of how much matter that object is made from.

matter Something that occupies space and has mass. Anything on Earth with matter will have a property described as "weight."

media (in the social sciences) A term for the ways information is delivered and shared within a society. It encompasses not only the traditional media — newspapers, magazines, radio and television — but also Internet- and smartphone-based outlets, such as blogs, Twitter, Facebook and more. The newer, digital media are sometimes referred to as social media. The singular form of this term is medium.

Milky Way The galaxy in which Earth’s solar system resides.

NASA Short for the National Aeronautics and Space Administration. Created in 1958, this U.S. agency has become a leader in space research and in stimulating public interest in space exploration. It was through NASA that the United States sent people into orbit and ultimately to the moon. It also has sent research craft to study planets and other celestial objects in our solar system.

observatory (in astronomy) The building or structure (such as a satellite) that houses one or more telescopes.

online (n.) On the internet. (adj.) A term for what can be found or accessed on the internet.

paradox An idea or a statement that is true, but that seems logically impossible.

particle A minute amount of something.

perception The state of being aware of something — or the process of becoming aware of something — through use of the senses.

physical (adj.) A term for things that exist in the real world, as opposed to in memories or the imagination. It can also refer to properties of materials that are due to their size and non-chemical interactions (such as when one block slams with force into another).

physics The scientific study of the nature and properties of matter and energy. Classical physics is an explanation of the nature and properties of matter and energy that relies on descriptions such as Newton’s laws of motion. Quantum physics, a field of study that emerged later, is a more accurate way of explaining the motions and behavior of matter. A scientist who works in such areas is known as a physicist.

quasar Short for quasi-stellar light source. This is the brilliant core of some galaxy (massive collections of stars) that contains a super-massive black hole. As mass from the galaxy is pulled into that black hole, a huge quantity of energy is released, giving the quasar its light.

radiation (in physics) One of the three major ways that energy is transferred. (The other two are conduction and convection.) In radiation, electromagnetic waves carry energy from one place to another. Unlike conduction and convection, which need material to help transfer the energy, radiation can transfer energy across empty space.

radio waves Waves in a part of the electromagnetic spectrum. They are a type that people now use for long-distance communication. Longer than the waves of visible light, radio waves are used to transmit radio and television signals. They also are used in radar.

relativity (in physics) A theory developed by physicist Albert Einstein showing that neither space nor time are constant, but instead affected by one’s velocity and the mass of things in your vicinity.

simulation (v. simulate) An analysis, often made using a computer, of some conditions, functions or appearance of a physical system. A computer program would do this by using mathematical operations that can describe the system and how it might change over time or in response to different anticipated situations.

spacetime A term made essential by Einstein’s theory of relativity, it describes a designation for some spot given in terms of its three-dimensional coordinates in space, along with a fourth coordinate corresponding to time.

spherical Adjective for something that is round (as a sphere).

star The basic building block from which galaxies are made. Stars develop when gravity compacts clouds of gas. When they become dense enough to sustain nuclear-fusion reactions, stars will emit light and sometimes other forms of electromagnetic radiation. The sun is our closest star.

stellar An adjective that means of or relating to stars.

sun The star at the center of Earth’s solar system. It’s an average size star about 26,000 light-years from the center of the Milky Way galaxy. Also a term for any sunlike star.

telescope Usually a light-collecting instrument that makes distant objects appear nearer through the use of lenses or a combination of curved mirrors and lenses. Some, however, collect radio emissions (energy from a different portion of the electromagnetic spectrum) through a network of antennas.

theoretical An adjective for an analysis or assessment of something that based on pre-existing knowledge of how things behave. It is not based on experimental trials. Theoretical research tends to use math — usually performed by computers — to predict how or what will occur for some specified series of conditions. Experimental testing or observations of natural systems will then be needed to confirm what had been predicted.

theory (in science) A description of some aspect of the natural world based on extensive observations, tests and reason. A theory can also be a way of organizing a broad body of knowledge that applies in a broad range of circumstances to explain what will happen. Unlike the common definition of theory, a theory in science is not just a hunch. Ideas or conclusions that are based on a theory — and not yet on firm data or observations — are referred to as theoretical. Scientists who use mathematics and/or existing data to project what might happen in new situations are known as theorists.

universe The entire cosmos: All things that exist throughout space and time. It has been expanding since its formation during an event known as the Big Bang, some 13.8 billion years ago (give or take a few hundred million years).

wave A disturbance or variation that travels through space and matter in a regular, oscillating fashion.

World War I Also known as WWI and the Great War. This war began in 1914, as two alliances faced off against one another. On one side were the so-called Central Powers — Germany, Bulgaria and the Ottoman and Austro-Hungarian empires. On the other side were the Allies — France, Great Britain, Russia, Italy and, beginning in 1917, the United States.

X-ray A type of radiation analogous to gamma rays, but having somewhat lower energy.