Astronomy

How small would you have to crush an object for it to become a black hole?

How small would you have to crush an object for it to become a black hole?


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I was wondering how much you had to crush an object for it to become a black hole. Recently I learned that anything could become a black hole (even you) if it were crushed down small enough, for example our sun would have to be crushed to the size of Manhattan to become a black hole (According to a video I saw). I did a little research and found out that something would have to be crushed down to Schwarzchild radius meaning all of that objects mass would have to be crushed into that objects radius. But if you say crush the sun down to the size of Manhattan, that is much smaller than the sun's actual radius. So I haven't really gotten a clear answer and I'm a little confused, thanks for clarifying =)


Well, I wasn't going to answer but the other two answers are wrong, or at least incomplete. If you wish to make a black hole from a stellar-sized object, then there is no need to compress it to as small as the Schwarzschild radius (though that would certainly work and would certainly be the answer for smaller objects with negligible self-gravity). Instead, you just need to compress it to a size at which it cannot be possibly supported by any plausible equation of state against further gravitational collapse. It turns out that this is somewhat bigger than the Schwarzschild radius and hence the density required is considerably lower. More details below.

There is a radius, larger than the Schwarzschild radius at which a neutron star, quark matter, whatever its equation of state, cannot be supported against collapse.

There are limits imposed by causality and General Relativity on the structure of compact stars. In "Black Holes, White Dwarfs and Neutron Stars" by Shapiro & Teukolsky, pp.260-261, it is shown, approximately, that even if the equation of state hardens to the point where the speed of sound equals the speed of light, that $(GM/Rc^2)<0.405$.

The Schwarzschild radius is $R_s=2GM/c^2$ and therefore $R > 1.23 R_s$ for stability. This limit is reached for a neutron star with $M simeq 3.5 M_{odot}$. A more accurate treatment in Lattimer (2013) suggests that a maximally compact neutron star has $Rgeq 1.41R_s$.

If the equation of state is softer, then collapse will occur at smaller masses, and higher densities but at a similar multiple of $R_s$.

Thus it is not necessary to compress matter within $R_s$ to form a black hole.

The picture below (from Demorest et al. 2010) shows the mass-radius relations for a wide variety of equations of state. The limits in the top-left of the diagram indicate the limits imposed by (most stringently) the speed of sound being the speed of light (labelled "causality" and which gives radii slightly larger than Shapiro & Teukolsky's approximate result) and then in the very top left, the border marked by "GR" coincides with the Schwarzschild radius. Neutron stars become unstable where their mass-radius curves peak, so stable neutron stars are always significantly larger than $R_s$ at all masses.


Well, it has to be crushed (compressed would be the better word to use here) below the Schwarzschild radius.

The Schwarzschild radius is the radius of the object in which the escape velocity would be the speed of light from that object. When this radius becomes even smaller, even light cannot escape it and voilà, there's your black hole!


$$r_s = frac{2GM}{c^2}$$ --Here:

$r_s$ is the Schwarzschild radius;
$G$ is the gravitational constant;
$M$ is the mass of the object;
$c$ is the speed of light in vacuum.

The proportionality constant, $2G/c^2$, is approximately 1.48×1027 m/kg


Why the sun won't become a black hole

NASA’s Solar Dynamics Observatory captured this view of a solar eruption on April 21, 2015. Credit: NASA/SDO

Will the sun become a black hole? No, it's too small for that!

The sun would need to be about 20 times more massive to end its life as a black hole. Stars that are born this size or larger can explode into a supernova at the end of their lifetimes before collapsing back into a black hole, an object with a gravitational pull so strong that nothing, not even light, can escape. Some smaller stars are big enough to go supernova, but too small to become black holes—they'll collapse into super-dense structures called neutron stars after exploding as a supernova. But the sun's not big enough for this fate, either: It has only about one-tenth of the mass needed to eventually become a neutron star.

So what will happen to the sun? In some 6 billion years it will end up as a white dwarf—a small, dense remnant of a star that glows from leftover heat. The process will start about 5 billion years from now when the sun begins to run out of fuel.

Like most stars, during the main phase of its lifetime, the sun creates energy by fusing hydrogen atoms in its core. In about 5 billion years, the sun will start to run out of hydrogen in its core to fuse, and it will begin to collapse. This will let the sun start to fuse heavier elements in the core, along with fusing hydrogen in a shell wrapped around the core. When this happens, the sun's temperature will increase, and the outer layers of the sun's atmosphere will expand so far out into space that they'll engulf Earth. (This would make Earth uninhabitable for life as we know it—though other factors in planetary evolution might make it uninhabitable before that point.) This is the red giant phase, and it will last about a billion years, before the sun collapses into a white dwarf.


Journey through a wormhole

"Interstellar" is set at some nebulous point in the not-too-distant future, when global crop failures threaten humanity with extinction. So a small band of explorers, led by a pilot-turned-farmer named Cooper (McConaughey), blasts off to search for an exoplanet that could serve as a new home for the human race.

The astronauts are aided in their quest by a wormhole &mdash a sort of tunnel that allows relatively quick travel between widely separated parts of the universe &mdash which had mysteriously appeared near Saturn some years before. Cooper steers the pioneers' ship, called Endurance, through the wormhole into a planet-rich portion of a faraway galaxy.

Though wormholes are a favored sci-fi trope, nobody knows whether or not they actually exist. According to Einstein's theory of general relativity, they are possible, but no sign of them has ever been spotted.

Furthermore, scientists say, a wormhole would likely collapse quickly unless it was propped open using some kind of negative-energy matter. So the big wormhole in "Interstellar" would require some serious and exotic engineering work &mdash but I'll stop here, so I don't give too much away about the film.

The "Interstellar" visual-effects team used equations provided by Thorne to come up with their representation of the wormhole, depicting its entrance as a shimmering sphere &mdash just as it likely would look in real life, Thorne said.

"Neither wormholes nor black holes have been depicted in any Hollywood movie in the way that they actually would appear," Thorne said recently in an "Interstellar" science video produced by Wired magazine. "This is the first time the depiction began with Einstein's general relativity equations."


Where do black holes lead?

So there you are, about to leap into a black hole. What could possibly await should — against all odds — you somehow survive? Where would you end up and what tantalising tales would you be able to regale if you managed to clamber your way back?

The simple answer to all of these questions is, as Professor Richard Massey explains, "Who knows?" As a Royal Society research fellow at the Institute for Computational Cosmology at Durham University, Massey is fully aware that the mysteries of black holes run deep. "Falling through an event horizon is literally passing beyond the veil — once someone falls past it, nobody could ever send a message back," he said. "They'd be ripped to pieces by the enormous gravity, so I doubt anyone falling through would get anywhere."

If that sounds like a disappointing — and painful — answer, then it is to be expected. Ever since Albert Einstein's general theory of relativity was considered to have predicted black holes by linking space-time with the action of gravity, it has been known that black holes result from the death of a massive star leaving behind a small, dense remnant core. Assuming this core has more than roughly three-times the mass of the sun, gravity would overwhelm to such a degree that it would fall in on itself into a single point, or singularity, understood to be the black hole's infinitely dense core.

The resulting uninhabitable black hole would have such a powerful gravitational pull that not even light could avoid it. So, should you then find yourself at the event horizon — the point at which light and matter can only pass inward, as proposed by the German astronomer Karl Schwarzschild — there is no escape. According to Massey, tidal forces would reduce your body into strands of atoms (or 'spaghettification', as it is also known) and the object would eventually end up crushed at the singularity. The idea that you could pop out somewhere — perhaps at the other side — seems utterly fantastical.

What about wormholes?

Or is it? Over the years scientists have looked into the possibility that black holes could be wormholes to other galaxies. They may even be, as some have suggested, a path to another universe.

Such an idea has been floating around for some time: Einstein teamed up with Nathan Rosen to theorise bridges that connect two different points in space-time in 1935. But it gained some fresh ground in the 1980s when physicist Kip Thorne — one of the world's leading experts on the astrophysical implications of Einstein's general theory of relativity — raised a discussion about whether objects could physically travel through them.

"Reading Kip Thorne's popular book about wormholes is what first got me excited about physics as a child," Massey said. But it doesn't seem likely that wormholes exist.

Indeed, Thorne, who lent his expert advice to the production team for the Hollywood movie Interstellar, wrote: "We see no objects in our universe that could become wormholes as they age," in his book "The Science of Interstellar" (W.W. Norton and Company, 2014). Thorne told Space.com that journeys through these theoretical tunnels would most likely remain science fiction, and there is certainly no firm evidence that a black hole could allow for such a passage.

But, the problem is that we can't get up close to see for ourselves. Why, we can't even take photographs of anything that takes place inside a black hole — if light cannot escape their immense gravity, then nothing can be snapped by a camera. As it stands, theory suggests that anything which goes beyond the event horizon is simply added to the black hole and, what's more, because time distorts close to this boundary, this will appear to take place incredibly slowly, so answers won't be quickly forthcoming.

"I think the standard story is that they lead to the end of time," said Douglas Finkbeiner, professor of astronomy and physics at Harvard University. "An observer far away will not see their astronaut friend fall into the black hole. They'll just get redder and fainter as they approach the event horizon [as a result of gravitational red shift]. But the friend falls right in, to a place beyond 'forever.' Whatever that means."

Maybe a black hole leads to a white hole

Certainly, if black holes do lead to another part of a galaxy or another universe, there would need to be something opposite to them on the other side. Could this be a white hole — a theory put forward by Russian cosmologist Igor Novikov in 1964? Novikov proposed that a black hole links to a white hole that exists in the past. Unlike a black hole, a white hole will allow light and matter to leave, but light and matter will not be able to enter.

Scientists have continued to explore the potential connection between black and white holes. In their 2014 study published in the journal Physical Review D, physicists Carlo Rovelli and Hal M. Haggard claimed that "there is a classic metric satisfying the Einstein equations outside a finite space-time region where matter collapses into a black hole and then emerges from a while hole." In other words, all of the material black holes have swallowed could be spewed out, and black holes may become white holes when they die.

Far from destroying the information that it absorbs, the collapse of a black hole would be halted. It would instead experience a quantum bounce, allowing information to escape. Should this be the case, it would shed some light on a proposal by former Cambridge University cosmologist and theoretical physicist Stephen Hawking who, in the 1970s, explored the possibility that black holes emit particles and radiation — thermal heat — as a result of quantum fluctuations.

"Hawking said a black hole doesn't last forever," Finkbeiner said. Hawking calculated that the radiation would cause a black hole to lose energy, shrink and disappear, as described in his 1976 paper published in Physical Review D. Given his claims that the radiation emitted would be random and contain no information about what had fallen in, the black hole, upon its explosion, would erase loads of information.

This meant Hawking's idea was at odds with quantum theory, which says information can't be destroyed. Physics states information just becomes more difficult to find because, should it become lost, it becomes impossible to know the past or the future. Hawking's idea led to the 'black hole information paradox' and it has long puzzled scientists. Some have said Hawking was simply wrong, and the man himself even declared he had made an error during a scientific conference in Dublin in 2004.

So, do we go back to the concept of black holes emitting preserved information and throwing it back out via a white hole? Maybe. In their 2013 study published in Physical Review Letters, Jorge Pullin at Louisiana State University and Rodolfo Gambini at the University of the Republic in Montevideo, Uruguay, applied loop quantum gravity to a black hole and found that gravity increased towards the core but reduced and plonked whatever was entering into another region of the universe. The results gave extra credence to the idea of black holes serving as a portal. In this study, singularity does not exist, and so it doesn't form an impenetrable barrier that ends up crushing whatever it encounters. It also means that information doesn't disappear.

Maybe black holes go nowhere

Yet physicists Ahmed Almheiri, Donald Marolf, Joseph Polchinski and James Sully still believed Hawking could have been on to something. They worked on a theory that became known as the AMPS firewall, or the black hole firewall hypothesis. By their calculations, quantum mechanics could feasibly turn the event horizon into a giant wall of fire and anything coming into contact would burn in an instant. In that sense, black holes lead nowhere because nothing could ever get inside.

This, however, violates Einstein's general theory of relativity. Someone crossing the event horizon shouldn't actually feel any great hardship because an object would be in free fall and, based on the equivalence principle, that object — or person — would not feel the extreme effects of gravity. It could follow the laws of physics present elsewhere in the universe, but even if it didn't go against Einstein's principle it would undermine quantum field theory or suggest information can be lost.

Black hole of uncertainty

Step forward Hawking once more. In 2014, he published a study in which he eschewed the existence of an event horizon — meaning there is nothing there to burn — saying gravitational collapse would produce an 'apparent horizon' instead.

This horizon would suspend light rays trying to move away from the core of the black hole, and would persist for a "period of time." In his rethinking, apparent horizons temporarily retain matter and energy before dissolving and releasing them later down the line. This explanation best fits with quantum theory — which says information can't be destroyed — and, if it was ever proven, it suggests that anything could escape from a black hole.

Hawking went as far as saying black holes may not even exist. "Black holes should be redefined as metastable bound states of the gravitational field," he wrote. There would be no singularity, and while the apparent field would move inwards due to gravity, it would never reach the center and be consolidated within a dense mass.

And yet anything which is emitted will not be in the form of the information swallowed. It would be impossible to figure out what went in by looking at what is coming out, which causes problems of its own — not least for, say, a human who found themselves in such an alarming position. They'd never feel the same again!

One thing's for sure, this particular mystery is going to swallow up many more scientific hours for a long time to come. Rovelli and Francesca Vidotto recently suggested that a component of dark matter could be formed by remnants of evaporated black holes, and Hawking's paper on black holes and 'soft hair' was released in 2018, and describes how zero-energy particles are left around the point of no return, the event horizon — an idea that suggests information is not lost but captured.

This flew in the face of the no-hair theorem which was expressed by physicist John Archibald Wheeler and worked on the basis that two black holes would be indistinguishable to an observer because none of the special particle physics pseudo-charges would be conserved. It's an idea that has got scientists talking, but there is some way to go before it's seen as the answer for where black holes lead. If only we could find a way to leap into one.


Black holes vs. wormholes

Gravitational-wave observatories have detected more than 20 giant collisions between extraordinarily dense and massive objects such as black holes and neutron stars. However, more exotic objects may theoretically exist, such as wormholes, the collisions of which should also produce gravitational signals that scientists could detect.

Wormholes are tunnels in spacetime that, in theory, can allow travel anywhere in space and time, or even into another universe. Einstein's theory of general relativity allows for the possibility of wormholes, although whether they really exist is another matter.

In principle, all wormholes are unstable, closing the instant they open. The only way to keep them open and traversable is with an exotic form of matter with so-called "negative mass." Such exotic matter has bizarre properties, including flying away from a standard gravitational field instead of falling toward it like normal matter. No one knows if such exotic matter actually exists.

In many ways, a wormhole resembles a black hole. Both types of objects are extraordinarily dense and have powerful gravitational pulls for objects their size. The main difference is that no object can theoretically get back out after entering a black hole's event horizon &mdash the threshold where the speed needed to escape the black hole's gravitational pull exceeds the speed of light &mdash whereas any object entering a wormhole could theoretically reverse course.

Assuming wormholes might exist, scientists investigated the gravitational signals generated when a black hole orbits a wormhole for a new paper, which has not yet been peer-reviewed. The researchers also explored what might happen when the black hole enters one mouth of the wormhole, exits out the wormhole's other mouth into another point in space-time, and then &mdash assuming the black hole and wormhole are gravitationally bound to one another &mdash falls back into the wormhole and emerges out the other side.


A Trip into a Black Hole

The fact that scientists cannot see inside black holes has not kept them from trying to calculate what they are like. One of the first things these calculations showed was that the formation of a black hole obliterates nearly all information about the star that collapsed to form it. Physicists like to say “black holes have no hair,” meaning that nothing sticks out of a black hole to give us clues about what kind of star produced it or what material has fallen inside. The only information a black hole can reveal about itself is its mass, its spin (rotation), and whether it has any electrical charge.

What happens to the collapsing star-core that made the black hole? Our best calculations predict that the material will continue to collapse under its own weight, forming an infinitely squozen point—a place of zero volume and infinite density—to which we give the name singularity. At the singularity, spacetime ceases to exist. The laws of physics as we know them break down. We do not yet have the physical understanding or the mathematical tools to describe the singularity itself, or even if singularities actually occur. From the outside, however, the entire structure of a basic black hole (one that is not rotating) can be described as a singularity surrounded by an event horizon. Compared to humans, black holes are really very simple objects.

Scientists have also calculated what would happen if an astronaut were to fall into a black hole. Let’s take up an observing position a long, safe distance away from the event horizon and watch this astronaut fall toward it. At first he falls away from us, moving ever faster, just as though he were approaching any massive star. However, as he nears the event horizon of the black hole, things change. The strong gravitational field around the black hole will make his clocks run more slowly, when seen from our outside perspective.

If, as he approaches the event horizon, he sends out a signal once per second according to his clock, we will see the spacing between his signals grow longer and longer until it becomes infinitely long when he reaches the event horizon. (Recalling our discussion of gravitational redshift, we could say that if the infalling astronaut uses a blue light to send his signals every second, we will see the light get redder and redder until its wavelength is nearly infinite.) As the spacing between clock ticks approaches infinity, it will appear to us that the astronaut is slowly coming to a stop, frozen in time at the event horizon.

In the same way, all matter falling into a black hole will also appear to an outside observer to stop at the event horizon, frozen in place and taking an infinite time to fall through it. But don’t think that matter falling into a black hole will therefore be easily visible at the event horizon. The tremendous redshift will make it very difficult to observe any radiation from the “frozen” victims of the black hole.

This, however, is only how we, located far away from the black hole, see things. To the astronaut, his time goes at its normal rate and he falls right on through the event horizon into the black hole. (Remember, this horizon is not a physical barrier, but only a region in space where the curvature of spacetime makes escape impossible.)

You may have trouble with the idea that you (watching from far away) and the astronaut (falling in) have such different ideas about what has happened. This is the reason Einstein’s ideas about space and time are called theories of relativity. What each observer measures about the world depends on (is relative to) his or her frame of reference. The observer in strong gravity measures time and space differently from the one sitting in weaker gravity. When Einstein proposed these ideas, many scientists also had difficulty with the idea that two such different views of the same event could be correct, each in its own “world,” and they tried to find a mistake in the calculations. There were no mistakes: we and the astronaut really would see him fall into a black hole very differently.

For the astronaut, there is no turning back. Once inside the event horizon, the astronaut, along with any signals from his radio transmitter, will remain hidden forever from the universe outside. He will, however, not have a long time (from his perspective) to feel sorry for himself as he approaches the black hole. Suppose he is falling feet first. The force of gravity that the singularity exerts on his feet is greater than on his head, so he will be stretched slightly. Because the singularity is a point, the left side of his body will be pulled slightly toward the right, and the right slightly toward the left, bringing each side closer to the singularity. The astronaut will therefore be slightly squeezed in one direction and stretched in the other. Some scientists like to call this process of stretching and narrowing spaghettification. The point at which the astronaut becomes so stretched that he perishes depends on the size of the black hole. For black holes with masses billions of times the mass of the Sun, such as those found at the centers of galaxies, the spaghettification becomes significant only after the astronaut passes through the event horizon. For black holes with masses of a few solar masses, the astronaut will be stretched and ripped apart even before he reaches the event horizon.

Earth exerts similar tidal forces on an astronaut performing a spacewalk. In the case of Earth, the tidal forces are so small that they pose no threat to the health and safety of the astronaut. Not so in the case of a black hole. Sooner or later, as the astronaut approaches the black hole, the tidal forces will become so great that the astronaut will be ripped apart, eventually reduced to a collection of individual atoms that will continue their inexorable fall into the singularity.

From the previous discussion, you will probably agree that jumping into a black hole is definitely a once-in-a-lifetime experience! You can see an engaging explanation of death by black hole by Neil deGrasse Tyson, where he explains the effect of tidal forces on the human body until it dies by spaghettification.

Key Concepts and Summary

Theory suggests that stars with stellar cores more massive than three times the mass of the Sun at the time they exhaust their nuclear fuel will collapse to become black holes. The surface surrounding a black hole, where the escape velocity equals the speed of light, is called the event horizon, and the radius of the surface is called the Schwarzschild radius. Nothing, not even light, can escape through the event horizon from the black hole. At its center, each black hole is thought to have a singularity, a point of infinite density and zero volume. Matter falling into a black hole appears, as viewed by an outside observer, to freeze in position at the event horizon. However, if we were riding on the infalling matter, we would pass through the event horizon. As we approach the singularity, the tidal forces would tear our bodies apart even before we reach the singularity.

Glossary

a region in spacetime where gravity is so strong that nothing—not even light—can escape

event horizon:

a boundary in spacetime such that events inside the boundary can have no effect on the world outside it—that is, the boundary of the region around a black hole where the curvature of spacetime no longer provides any way out

singularity:

the point of zero volume and infinite density to which any object that becomes a black hole must collapse, according to the theory of general relativity


‘A black hole has no hair’

On March 28, 2011, astronomers detected a long gamma ray burst coming from the center of a galaxy 4 billion light-years away. This was the first time humans observed what might have been a dormant black hole eating a star.

No matter what a black hole eats — a star, a donkey, an iPhone, your grammar teacher — it’s all the same to the black hole. “A black hole has no hair,” the physicist John Archibald Wheeler once said, meaning that a black hole remembers only the mass, spin and charge of its dinner.

The more a black hole eats, the more it grows. In 2011, scientists discovered one of the biggest black holes ever, more than 300 million light-years away. It weighs enough to have gobbled up 21 billion suns. Scientists want to know if the biggest black holes are the result of two holes merging or one hole eating a lot. But scientists don’t know how they grew so large.


5 Comments

Re speeding up to form a black hole: I’m no physicist, but remember that you need exponentially more energy to accelerate a particle close to the speed of light so it seems to me that by the time you reach a mass that would collapse, you’ve fed it enough energy that it has enough mass-energy to collapse without acceleration.

I am not a physicist or scientist, just interested. But would a 1kg stationery mass object act like a black hole if accelerated to a speed close to the speed of light – due to its enormous increase in relativistic mass?
Will nearby objects like planets and stars get sucked into it, like they get sucked into a “normal” black hole?
I suspect not, for the following reasons:
(a) If this object came flying through our solar system (for example), then it would come and go *so quickly* that the gravitational force would not have time to suck the planets and our sun into it. This is because the gravitational force can’t travel faster than the speed of light. So the object would be out of effective range before the planets had time to do more than a brief wobble, I suspect.
(b) In the case that other objects were travelling alongside the flying object at a similar speed in the same direction, then these other objects would also gain relativistic mass. So *all* these objects would be exerting enormous gravitational forces on each other. Again this is very different to the situation of a “normal” black hole, which is surrounded by much less massive objects that it can easily suck in.
What about photons of light travelling in the same direction at the same speed as the flying 1kg mass? Would these photons be sucked into the flying mass due to its huge relativistic mass? Perhaps. I don’t know enough about photons. They seem to be very mysterious to me, travelling at the speed of light yet not appearing to possess much in the way of mass themselves. I don’t really understand photons at all.

Re: Mass->fast->black hole
Yes, a fast moving mass would become a black hole. And slowing it down would stop it being a black hole.
The people on the cast seemed to be confusing a black hole with a singularity. This is an important difference. For example, (my pet theory) the universe ‘could’ be a black hole. To all intents and purposes it is, we cannot leave it and can transfer no knowledge out of it. And (this get close to ridiculous) the proof of it is that it is expanding at an increasing rate and that expansion must be fed by some energy which could be coming from an external mass that our black hole universe is feeding on. Or not.
Point is – black hole is simply a region of space that (even) light cannot escape from.
A singularity is completely different, essentially a point in space with infinite gravity.
So all singularities must be black holes, but not all black holes are singularities.

I note that Pamela and the commentators are careful to add the qualification “relativistic” to this type of “mass,” to distinguish it from what has elsewhere been called “proper mass,” the mass that is determined by atom-content. Surely there’s a point to the distinction. Who’s to say that both types of “mass” have the same set of properties? If we look at the evidence that is taken as experimental validation for the increase in “relativistic mass” – we find that it consists in an observed decrease in acceleration at the high velocities obtainable in particle accelerators. Maybe I’ve missed something, but I am unaware of any reports that the relevant data contain any traces of evidence for light-bending effects such as those observed near massive objects in the universe – objects with large _proper_ masses, that is – these light-bending effects being a key step in the reasoning that leads to black holes. In a way it would be “unfair” to expect such evidence from the accelerator data, since the “relativistic” masses thus obtained are presumably of nowhere near comparable magnitude to astronomical objects. But still that leaves us without observational evidence that the two types of “mass” are comparable in this respect.
In fact, one can go further in criticizing the whole notion of “relativistic mass” – and therefore the presumption that it is reasonable to expect identical effects to those associated with mass proper. I think no one said it better than D.B. Larson:
“Conclusions outside the scope of the observations are not knowledge.
“Somewhat analogous to the practice of extrapolation, but of a more questionable character, is the practice of exaggeration that is, claiming more than what the observations or measurements actually substantiate. A classic example is Einstein’s theory that mass is a function of velocity. Throughout scientific literature this theory is described as having been ‘proved’ by the results of experiment and by the successful use of the predictions of the theory in the design of the particle accelerators. Yet at the same time that a host of scientific authorities are proclaiming this theory as firmly established and incontestable experimental fact, practically every elementary physics textbook admits that it is actually nothing more than an arbitrary selection from among several possible alternative explanations of the observed facts. The experiments simply show that if a particle is subjected to an unchanged electric or magnetic force, the resulting acceleration decreases at high velocities and approaches a limit of zero at the velocity of light. The further conclusion that the decrease in acceleration is due to an increase in mass is a pure assumption that has no factual foundation whatever.
“As one textbook author explains the situation: “There seems to be no reason to believe that there is any change in the charge, and we therefore conclude that the mass increases.” Another says: “This decrease is interpreted as in increase of mass with speed, charge being constant.” Obviously an interpretation of the observed facts is not a fact in itself, and it is rather strange that the theorists have been so eager to accept this particular interpretation that they have not even taken the time to examine the full range of possible alternative interpretations. As these quotations from the textbooks indicate, it has been taken for granted that either the charge or the mass must be variable, but actually it is the acceleration that has been measured, and the acceleration is a relation of force to mass, not of charge to mass. The accepted interpretations of the observed facts therefore contain the additional assumption that the effective force exerted by a charge is constant irrespective of the velocity of the object to which it is applied. The possibility that this assumption is invalid cannot logically be excluded from consideration on the contrary, there are some distinct advantages in maintaining both charge and mass as constant magnitudes. When we get down to bedrock it is clear that the theory of an increase in mass is not something that has been proved by experiment, as is so widely claimed it is a pure assumption that goes beyond the scope of the experiment, and is only one of several possible alternatives. Any theory which leads to the observed decrease in acceleration at high velocities is equally as consistent with the observed facts as Einstein’s theory that the mass increases.”
From D.B. Larson, “Just How Much Do We Really Know?,” 1961:
http://library.rstheory.org/articles/Larson/JustHowMuch.html

I don’t drink, but if I did, a good drinking game would be to take a shot every time they say “black hole” in the questions show.


DETECTING BLACK HOLES

If a black hole exists in a close binary system, it can be detected indirectly. Gas ripped from the companion star will spiral in toward the black hole. As it does so, it is heated up (by tidal heating, and by friction as it rubs against neighboring gas). The hot gas emits X-rays as it undergoes its death spiral to the event horizon. (Once it's inside the event horizon, we don't see the gas any more, but it's highly visible as long as it's outside.) If you are hunting for black holes, it's good to start by looking for binary star systems which are also strong X-ray sources.

To demonstrate typical techniques for deducing the existence of black holes, I will use the story of Cygnus X-1 as a case study. Cygnus X-1 is the brightest X-ray source in the constellation Cygnus. (Also known as the ``Northern Cross'', Cygnus is visible in the summer sky.) X-rays from Cygnus X-1 are seen to vary irregularly - in strong contrast to the regular pulses emitted by X-ray pulsars. The X-rays from Cygnus X-1 can grow substantially brighter or dimmer over time scales as short as 0.01 second. The natural deduction from the rapid variability of Cygnus X-1 is that the X-rays are coming from a region less than 0.01 light-second across. (0.01 light-second is 3000 kilometers, or roughly the diameter of the Earth's Moon.)

The position of the X-ray source Cygnus X-1 coincides with that of a star called HDE 226868. (The fact that it has a boring catalog number instead of a name like ``Alpha Cygni'' will tell you that the apparent brightness of HDE 226868 is not very high.) The spectrum of HDE 226868 reveals that it is a hot blue supergiant. Its mass, if it's a supergiant star, must be substantial it's estimated to be about 30 solar masses. The distance to HDE 226868 is estimated to be 2500 parsecs. Stars (even hot supergiant stars) don't produce a significant amount of X-rays their photospheres just aren't hot enough. However, when the spectrum of HDE 226868 is examined, it has the characteristic Doppler shifts of a star in a binary system. The star HDE 226868 is part of a binary star system with an orbital period of 5.6 days. The mass of the unseen companion to HDE 226868 must be, from an application of Kepler's Third Law, at least 7 solar masses.

Astronomers deduce that the unseen companion to HDE 226868 must be the X-ray source Cygnus X-1. Cygnus X-1 is too compact to be a star. It is too massive to be a white dwarf or a neutron star. Anything so compact and so massive must be a black hole. (For more about Cygnus X-1 and other black hole candidates, try the ``Imagine the Universe'' site, sponsored by Goddard Space Flight Center.

(3) Many galaxies, including our own, have a supermassive black hole at their center.

An interesting recent development in astronomy is that supermassive black holes (that is, black holes more than a million times the mass of the Sun) are found at the centers of many galaxies. Our own galaxy, for instance, has a black hole with mass 2.6 million Msun at its center, 8000 parsecs away from us. Our own galactic black hole is actually fairly wimpy. The Andromeda Galaxy, 700,000 parsecs away, has a black hole with a mass of 30 million Msun.


Ep. 18: Black Holes Big and Small

We’re finally ready to deal with the topic you’ve all been waiting for: Schwarzschild swirlers, Chandrasekhar crushers, ol’ matter manglers, sucking singularities… you might know them as black holes. Join as as we examine how black holes form, what they consume, and just how massive they can get.

Shownotes

General Information on Black Holes

    gravity’s relentless pull. An award winning interactive website covering a lot of FAQs, and the basics. Written and maintained by Robert Nemiroff (Michigan Technological University). Features explanations for general FAQs and links to interactive websites and movies. Black holes. by Ted Bunn (University of Richmond, then a grad student at University of California, Berkeley). The discussions of observations are out of date, but the theories haven’t changed much. scientists provide brief explanations about three different types of black holes, and link to many Chandra images and a short Chandra podcast.

Theorizing About Black Holes

Don’t forget to check out Astronomy Cast on the life cycle of stars, to understand how to get to black holes.

Transcript: Black Holes

Dr Pamela Gay: A black hole is basically an object that has shrunk down so small with all of its mass, that it’s actually possible to get close enough to all of that mass that you would have to go faster than the speed of light to get away from it. Our planet Earth is like a “people-hole� : no matter how hard I jump, I can’t jump off the surface of the planet. Well a black hole is an object that is so dense that its gravity so strong that light can’t get away from it.

Fraser: It’s a great analogy: the more massive an object gets, the stronger something has to be to escape, or the faster-moving something has to be to escape. With black holes it’s the speed of light, and as nothing moves faster than light, that’s that.

Pamela: Yes, you’re stuck! Now the catch is that any object, if you make it small enough, can become a black hole. The planet Earth would be a black hole if you could squish all its mass down to just a couple of millimetres across. It wouldn’t be a very impressive black hole, but if you got close enough you would be trapped on the Earth. But because the mass is spread out over such a large area, the gravitational effects aren’t that strong at the surface.

Fraser: So where did we come up with the idea of black holes?

Pamela: As far back as the 1784, the geologist John Michell started thinking “Well, we have this idea of Newtonian gravity, and we know about escape velocities, so let’s figure out just how big something has to be so that you have to go at the speed of light in order to escape.�

His calculation said that you had to have something about 500 times the radius of the Sun and the same density as the Sun at its surface to not be able to escape going at the speed of light. Physics has been upgraded since 1784 and we know that, with relativity, it’s a little more complicated. But the idea has been around for a long time.

Fraser: So what’s the more modern thinking about what’s going on inside a black hole?

Pamela: There are actually two different types of black hole there are those that are 4-15 times the size of the Sun, then there are those that are thousands of times the size of the Sun, while a stellar-mass black hole is a star that at some point just stopped producing the energy that supported the outer layers of the star. When those outer layers collapsed in, the particles could not support the weight of all of the material pressing down on them.

If you have an object of more than 1.4 Solar masses, when the mass collapses the protons and electrons smash together and all of them fuse into neutrons there is energy and bits escaping, but you end up with a neutron star.

If an object a little more than 3 solar masses collapses, it just keeps going, as neutrons (nor anything we can really understand) are not strong enough to hold the weight, so the star keeps collapsing. According to the math that we are working with today, you end up forming a singularity out of the material. But within the Schwarzschild radius…

Fraser: Sorry, what’s a singularity?

Pamela: Basically, it’s an infinitely dense point. You take all the matter and crush it down so it has basically no radius.

Fraser: So the pull of gravity is so strong that the matter is mashing the particles down to nothing?

Pamela: They basically reduce down to energy. Some people say it’s a “quark soupâ€?. We don’t fully understand the particle physics in this dense an environment. Our theories sort of stop once you get inside a black hole and there are some really powerful minds working on this, Stephen hawking, for instance.

Fraser: So what does Stephen Hawking think?

Pamela: Stephen Hawking is working on a theory of quantum gravity that is beyond the ability of anybody but the most intelligent experts in that field to understand, but there are indications that some really neat things are going on. For instance, there had been a long term bet between Hawking, Kip Thorn, and John Preskill about whether black holes consume information. One of the basic ideas of physics is that no information is ever lost and that, at a certain level, all of the information can somehow be gotten back.

But if stuff falls into a black hole never to come about again, that information is clearly getting absorbed into the black hole and lost forever. Or at least, that’s what people thought, but physics says information is never lost, so for a while there was a debate in which Thorn and Hawking said “Information is lost, black holes are uniqueâ€?, but Preskill said “No, information cannot be lost, that’s the rules of physicsâ€?.

Back in 2004, Hawking announced that maybe there were quantum perturbations at the event horizon of the black hole, and that information was able to come out through the stuff called “Hawking radiation�, or maybe there is information left behind if a black hole completely evaporates. This opens up fascinating things to talk about and he decided that information never is lost, so he paid Preskill in the form of a baseball encyclopaedia, with information he could always look up, as information is not lost.
Kip Thorn is still not convinced and has not yet paid his half of the bet, but these guys are doing complicated work to deal all the weird physics going on at the event horizon of a black hole.

Fraser: So, we have a star with 4-15 times the mass of the Sun, the fusion stops and it compresses down to possibly an infinitely small amount of space which we call a singularity, but it still maintains its mass. So what would we see if we were in the region of a black hole?

Pamela: If we were the poor schmuck who fell into the black hole, we would see ourselves falling in and all sorts of bad things would happen to us we would get stretched out, our body would be torn apart by the tidal forces of gravity being not as hard on our head as on our feet (if we were falling feet first) and this would all happen fairly rapidly, at least in our perspective.

But if we have a buddy a little further away, in a safe place not falling into the black hole, they would see us falling towards the black hole and continually slow down as we go, and get increasingly more red because the light coming from us would get red-shifted by the powerful gravity of the black hole. Eventually we would not be seen to fall into the black hole but – over an infinite amount of time – we would be seen to fade away.

Fraser: So the gravity of the black hole is stretching out the wavelengths of our light as it’s trying to escape the pull of the black hole.

Pamela: Yes, the light gets gravitationally red shifted because the wavelengths spread out.

Fraser: So you don’t actually disappear so much as fade away. Shouldn’t we be able to see black holes as very bright objects because they are surrounded by all the matter they have consumed?

Pamela: Actually, what is even brighter around black holes is their accretion disk. If something gets too close to a black hole, the material falling in will spiral around and form a disk of material. You get similar structures around white dwarf stars and neutron stars, as material falling into more or less any really compact object will form an accretion disk, which is so dense that there can be nuclear reactions going on within the disk. So, in some cases, this disk behaves almost like a star.

Fraser: So it’s as if the material is choking the black hole, which cannot eat it fast enough, so its backing up and the environment of this material becomes almost stellar in nature. It’s like when we talked about the first few moments of the Big Bang, when the whole universe was like the inside of a star.

Pamela: The conservation of angular momentum chokes the rate at which the material can fall into the black hole. It can’t just fall straight in unless it has a magically perfect trajectory (which never really happens). So the material gets choked up by the conservation of angular momentum and ends up creating this accretion disk which has amazing reactions going on within it, and that’s actually how we identify where we think black holes are located.

Fraser: That was going to be my next question: if black holes are black, how can we find them?

Pamela: We look for all the signatures of things can only happen near a black hole: rapidly rotating, highly dense accretion disks, and we can use the rate at which they are rotating to judge how massive the object at their centre has to be. So if you have a rapidly rotating accretion disk that indicates the mass within it is greater than about three solar masses, you have a pretty good clue that it probably has a black hole in the centre.

Fraser: Will it have a special signature that we can see in certain kinds of telescopes?

Pamela: These environments are generally so dense that the material gets so heated that we see x-ray emissions. So we can look for x-ray emissions as a signature of black holes.

Fraser: What about their mass? Does that have an effect on their local environment?

Pamela: That’s where the rotation rates come in. Things that are near a high mass object will orbit it much faster than those orbiting a low mass object at the same distance, so we look at something and see that the accretion disk is going super fast (mathematics, mathematics…!) and we can calculate the mass at the centre of the accretion disk, and using that mass we can figure out whether it’s a neutron star, a black hole or a white dwarf.

We can use Doppler shifts and measures of spectra to get at the rates of rotation (in the same way that a police officer can get the rate of how fast your car is going) and use that to identify where black holes are located.

Fraser: Earlier we talked about two sizes of black holes: stellar mass and those which are much larger. So what are those?

Pamela: There are also things called “supermassive black holes”that are somewhere between hundreds of thousands and tens of billions times bigger than our Sun.

Fraser: What percentage of the mass of a galaxy is that? There must be a big chunk of a galaxy just in that black hole.

Pamela: It’s a huge amount. These things form the core of galaxies, and the mass of a supermassive black hole in the centre of a galaxy is actually related to the size of the halo of a galaxy and how fast the stars within the galaxy are moving. These are basically the angry monster sitting at the core of every galaxy just waiting to feed on in-falling material.

Fraser: So there’s one at the heart of every galaxy?

Pamela: As far as we can tell, every galaxy has one in proportion to its size, and in fact, these things answer a lot of questions in astronomy quasars, for instance, are most likely black holes that are in the process of feeding on mass gas and dust that are falling into their centre.

Fraser: So that the backing up of material around the black hole?

Pamela: As the material falls in it gets lit up sometimes jets form, and it’s the jets that we can see in different types of objects. Active galactic nuclei, with amazing jets shooting out the ends, are black holes with jets which are just a side effect of the environment around the black hole.

Fraser: How come you get those jets?

Pamela: It’s this neat combination of what happens when you combine magnetic fields and in-falling material. Sometimes the material falls in along the ‘equator’ of the black hole and, as it falls, it gets twisted into the magnetic field and shot out the poles of the rotating black hole.

Fraser: What impact does one of these supermassive black holes have on its galaxy?

Pamela: The impact comes in terms of ending up with a huge central core shooting off huge amounts of radiation, but it’s localised to the core and the jets that are coming out of the poles. So you can still end up with star formation going on, and probably planet formation, just further from the centre. In fact our own Milky Way galaxy probably contained an active, consuming quasar black hole in its centre. We have the black hole today, it’s just not angrily feeding on dust and gas that’s falling into it.

Fraser: So we have a supermassive black hole at the middle of the Milky Way.

Pamela: And it’s not feeding on any gas and dust because there’s none falling into it today.

Fraser: So how was that discovered?

Pamela: Simply by looking at the stars. Andrea Ghez, Professor of Astronomy at the University of California, Los Angeles, took high speed images of the centre of the galaxy so that she could align and stack the images in such a way that she could look through the atmospheric crud, and the dust and gas between here and there, and actually see the stars that are very close to the centre.

Over the course of ten years, she could watch these stars move they would go half way round the centre of the galaxy while she was watching. Using the observed motions of these stars, she was able to calculate the mass of the object they had to be orbiting. Mathematically, it had to be a black hole (or some other object that no one has yet conceived of that is impossibly large and dense) that’s just sitting in the centre.

Fraser: There was a PBS special about three months ago where they showed the graphics that she built up. It was amazing to see the stars, several times the size of our Sun coming in then doing almost a quick turn around a point in space, then zooming back out, like comets orbiting the Sun, with bizarre orbits. I guess nothing could provide enough gravity but a supermassive black hole.

Pamela: There’s no way to pack enough normal stars into such a small area so as to get this gravitational effect. It’s one of the most breathtaking pieces of science to look at because you can see stars dramatically move like you would expect planets or comets – things local to our own solar system – to move.

Fraser: I’m sure people are going to want to know whether we are at any danger from these supermassive black holes at the heart of our galaxy.

Pamela: Absolutely none. We are safe!

Fraser: Not even a trillion years from now?

Pamela: Well, I really wouldn’t want to talk about a trillion years from now, because bad things are going to happen between now and then, like we are going to collide with the Andromeda galaxy, and then a lot of weird stuff is going to happen, because our supermassive black hole and Andromeda’s supermassive black hole will come together and orbit one another and perhaps even merge over time.

There are several merging galaxies where you can see these supermassive black holes near one another, with all the fabulous fireworks going off they trigger star formation, they have jets and they’re accreting matter. It’s fabulous fireworks! When we collide with another galaxy, I really can’t speak to our safety, but until that happens, I’m fairly certain we’re safe.

Fraser: Is our Sun going to turn into a black hole?

Pamela: No. Our Sun is just not fat enough. It’s just hanging out maintaining it’s weight quite nicely. It occasionally loses weight through mass loss, and the older it gets, the more mass it will lose through solar winds, and unless it finds some way (which physics cannot predict) to gain three times its current mass, we are totally safe.

Fraser: So what would happen if a black hole came through the solar system?

Pamela: We would die! Phil Plait from Bad Astronomy does a brilliant talk called “Seven Ways a Black Hole Can Kill You!” asking questions like “What would happen if a black hole did wander through the planet Earth, or through the Sun?â€? But we don’t know of any black holes that are going to do this, so we should be safe.

Fraser: Except they’re black and you can’t see them coming!

Pamela: Right, but they grab dust and gas as they go through it and light off fireworks as they go, so – as far as we know – we are totally safe from randomly wandering, isolated black holes.

Fraser: That’s good! Will black holes last forever is the end of the universe going to be when every piece of matter has found its way into a black hole?

Pamela: That’s one of the neat things black holes that are small enough can actually evaporate, just like water will evaporate from a glass after a time. But this is only true for small ones.

Fraser: But how does it evaporate?

Pamela: Throughout the universe, virtual particles are bubbling in and out of existence, so you can get an electron and a positron that spontaneously form and almost instantaneously come together and self annihilate. If these things form on the event horizon of a black hole, one may be on the outside of a black hole and be able to escape, while the other gets sucked in.

So the two never meet and annihilate one another, and you end up with particles bubbling up at the event horizon which escape the black hole and allow it to evaporate. This is called “Hawking Radiation�. If you have a big enough black hole, the amount of particles and energy that it absorbs just from the cosmic microwave background radiation is probably just enough to counteract the effects of evaporation, but small black holes can actually evaporate away.

Fraser: And then bigger black holes will eat those particles and everything will end up in the really big black holes.

Pamela: But there can still be things like white dwarfs, neutron stars and even rogue planets which never get close enough to a black hole to fall in. So it’s not that everything is going to be a black hole, but there will be a lot of them!

Fraser: Another grim future from Pamela! Thanks, that was great. Talk to you next week Pamela.