This new fusion process regularly happens with stars of more than 40 times the mass of our sun. Less-massive stars, though, end as neutron stars, where the special pressure of the degenerated particles in their interior suffices to counteract gravity.
If gravity wins, though, there is no end. The object shrinks more and more, until its density approaches infinite values. Today we call this a ‘singularity,’ for which the currently known laws of physics no longer apply. Space is curved so strongly that it collapses into itself, creating a hole in space-time, and any matter coming too close to this singularity can no longer escape. The radius within which this happens is called the ‘Schwarzschild radius,’ and the area that matter is not allowed to enter without being lost forever is called the ‘event horizon.’
Basically, any object possesses such an event horizon. The Schwarzschild radius of Earth is nine millimeters. But a black hole only develops if the entire mass of the object is located inside this radius. Therefore all the mass of Earth would have to be compressed to the size of a marble in order to turn it into a black hole!
Based on the known development process of a black hole, these objects should only exist in one specific class, the so-called ‘stellar black hole.’ Such remnants of dead stars weigh at least ten times the mass of the sun and have a Schwarzschild radius of 30 kilometers. So the entire mass of ten times our Sun is contained inside a sphere with approximately the diameter of the city of Berlin. That is amazing!
However, astronomers have proven that even more massive black holes exist. Sagittarius A*, at the center of the Milky Way, weighs as much as 4.3 million Suns! It belongs to the class of supermassive black holes. The record is almost ten times as much as Sagittarius A*. Generally, such giants (whose event horizons can be larger than our solar system!) are located in the center of a galaxy. It is assumed that they grew from normal types over the course of billions of years by accreting—a fancy term for accumulating via gravity—matter from their surroundings. The theoretical upper limit for a supermassive black hole is about 10 billion times the mass of the sun. At an even higher mass, equilibrium would form between the radiation pressure emitted by its immediate environs and the gravitation.
If black holes exist in the sizes M and XXL, there are bound to be intermediate sizes somewhere. (Think of clothing sizes where S stands for small, M for medium, L for large, and X for eXtra—large or small.) These intermediate black holes weigh between hundreds and thousands of times the mass of our Sun, but they are not easy to find. Stellar black holes can be detected by the remnants of supernova explosions around them. Supermassive black holes give off radiation, but intermediate ones offer few clues. Therefore there is no definite proof of their existence so far. What has been measured, though, are the echoes of mergers and collisions, during which these black holes are created and grow. The LIGO experiment has already detected several gravitational waves that were formed by the collisions of black holes. So we basically listened in on their unions, but haven’t yet caught them red-handed.
It gets even more complicated with the sizes S and XS. Shortly after the Big Bang, the universe was still very small and packed with matter and energy. Back then, 13.8 billion years ago, there should have been areas in which matter happened to be so densely distributed that the conditions for the creation of a black hole existed. In those cases, matter had no choice but to give in to gravitation and thus collapse. The so-called ‘primordial black holes’ created this way would be considerably smaller than the stellar class. They might be as heavy as the moon and have a Schwarzschild radius of one tenth of a millimeter. This would make them much harder to detect than any other kind. However, their lifespan would ‘only’ be in the range of the age of the universe. It might therefore be possible to prove not only their existence, but the end of their existence, which should be observable in the form of a gamma-ray burst. So far, though, none of the gamma-ray bursts measured in space have given any specific indications of having been caused by a dying primordial black hole.
The theoretical lower limit for the mass of a black hole lies below the smallest possible mass, the Planck mass. So there could also be holes that are size XS, or XXS, or even XXXXXXXS, all of which would be called black micro-holes. This has been mostly discussed in connection with the high-energy experiments using the Large Hedron Collider (LHC) accelerator at the CERN institute. What would happen if the conditions for a black hole developing in a tiny space were to be fulfilled there? Nothing. First of all, the lifespan of a micro-hole is very short. Secondly, its event horizon is tiny. Black holes are not like vacuum cleaners sucking up everything near them. They only swallow whatever crosses their event horizons - they cannot suck matter into their horizons. If such a horizon is much smaller than the average distance between two atoms, then the micro-hole starves and disappears after a short time.
Researchers have even calculated what an encounter with a considerably heavier primordial black hole would do to Earth. The black hole would speed through the planet within approximately a minute and cause weak earthquakes with a magnitude of less than 4. The shape of the pressure waves created would be unique, however, and unlike those that occur in normal quakes. Therefore, we would have seismological proof of an encounter with a primordial black hole. The probability is very low, though, and scientists only expect such a collision once every few million years.
How does one weigh a black hole? It is quite simple. You look at the galaxy in whose center the black hole is located. A research team at Swinburne University of Technology in Australia and the University of Minnesota/Duluth in the US compared numerous spiral galaxies and discovered a clear relationship between the mass of the black hole in its center and the way the galaxy presses its arms to itself.
According to this study, the looser it held its arm, the lighter the black hole must be. This only applied to spiral galaxies, though. If you want to calculate this for yourself, the formula is: log (MBH/M⊙) = (7.01 ± 0.07) − (0.171 ± 0.017)[| ϕ | − 15°], where ϕ is the angle with which the arm stretches into space, and MBH/M⊙ stands for the mass of the black hole compared to that of our sun.
The Life and Death of Black Holes
The birth of black holes has already been described above. However, they do not remain in the same state forever—they grow, and at some point they die.
The growth is driven by two processes, accretion of normal matter, and merging with other black holes. By now, astronomers can accurately observe and document both of these processes.
While black holes themselves do not emit any—or more precisely, hardly any—radiation, their accretion disks can be among the brightest objects in the universe. Material in the vicinity of black holes does not fall into them along a straight path.
Accretion disks do not form exclusively around black holes, they generally form around high-mass objects, so-called accretors. For example, young stars can be among them. If it is assumed that an object is initially surrounded by dust and gas in all directions, then why does a disk form? The reason is a constant interaction of two forces. Gravitation attempts to pull matter as close as possible. However, this leads to heat, which creates a counterpressure acting outward. Gravitation can only win if the cloud can somehow get rid of the heat. This is achieved by radiation, for which a disk offers the most efficient shape. Therefore, the original cloud gradually turns into a disk—this also applies to the creation of solar systems. Within the disk there is a constant transport of material from the outside in, while the angular momentum is transported outward. The disk has an inner edge, where it rotates almost at the speed of light. Material that gets any closer to the black hole is not able to hold on—the dust cannot go faster than the speed of light—and it finally falls into the hole.
At first it moves through the ‘ergosphere,’ an area outside of the event horizon. Here only photons survive, light particles that can endlessly rotate around the black hole. Further inside is the event horizon, the threshold to uncertainty.
With every particle that falls into it, the black hole becomes a bit larger and heavier. Currently, meaning 13.8 billion years after the Big Bang, this is the dominant process, at least for most black holes.
However, they can also lose mass via ‘Hawking radiation.’ You can guess who came up with that concept. In a vacuum, pairs of particles constantly appear out of nothing. This is no problem, since the conservation of energy is only briefly violated, and it can handle this. Normally, these virtual particles soon annihilate each other and pay off their energy debt.
But what would happen if one particle disappeared into the event horizon and the other one did not? Then someone else had to pay the debt—the black hole. The remaining particle is emitted as Hawking radiation and the hole loses a tiny bit of mass. The smaller the black hole, the shorter the wavelength of the radiation and the higher its energy content. Therefore, small black holes evaporate in a relatively short time, assumed to be a few billion years. Much larger black holes eventually dissolve, too, but that will take a very, very long time. Currently, the temperature of stellar black holes lies below the temperature of the background radiation. For this very reason they absorb more energy than they emit. Countless billions of years from now, black holes will be the last witnesses that the universe once contained something other than an even distribution of matter and energy. Unless, that is, the universe ends in a different, more spectacular fashion, like being destroyed in a collision with another universe.
The Oldest Black Hole
800 Million Suns. If you considered Sagittarius A*, the black hole at the center of the Milky Way, a big deal, you have to multiply this monster by 200... and then you get the mass of the black hole at the center of the quasar ULAS J134208.10+092838.61—its friends, many of whom are astronomers, as one would expect, are allowed to call it J1342+0928 for short. Quasars are radio galaxies, active siblings of the Milky Way that emit such huge amounts of energy, particularly in the radio range, that they are observable from Earth across very large distances.
J1342+0928 tops them all. With a red shift of z=7.54 this quasar set a new record and must therefore be located near the edge of the observable universe. That is not the reason, though, why researchers are so excited about its galaxy, which shines as brightly as 400 trillion suns! It is because its light took so long to reach us, and as such we can use it to glance back into the dawn of the cosmos. When the light that now reaches us was emitted, the universe was only 690 million years old, about five percent of its current age.
If one considered the universe to be an adult now, it would have been a teenager then, in the middle of adolescence and undergoing important changes, at least if the standard model about the evolution of the universe is correct. Astronomers have indeed found important traces of it. They managed to measure, with a high degree of certainty, a significant percentage of neutral hydrogen in the spectrum of the quasar. When the giant galaxy shone in all the splendor we can only now marvel at, the cosmos was in the reionization phase. During this, the hydrogen gas that had become neutral during the previous recombination era was robbed of its electrons and thus ionized by newly ignited stars and galaxies like J1342+0928. Researchers found that this process had not yet finished 690 million years after the Big Bang.
The fact that such a massive black hole existed even then, relatively soon after the Big Bang, gave cosmologists new information about the creation and growth of black holes. J1342+0928 was only possible because even at such an early date black holes with a mass of at least 10,000 suns developed—or did the black holes back then grow differently than we assume?
There is actually a limit for the increase in size, the so-called ‘Eddington limit.’ If too much material falls into a black hole, it chokes, so to speak, and cannot absorb anything else for a while. However, there are also models according to which a mass increase above the Eddington limit is possible.
How to Find Black Holes
In order to directly observe a black hole, one would have to get very close to it, as is the case in The Hole. Humans are hardly likely to be able to do so within the next thousand years. The Hawking radiation emitted by a hole is also too weak for a direct analysis.
However black holes can be observed using a different method, namely their effect on the area outside the event horizon. This effect takes on many forms. Therefore researchers now have a number of observation methods they can use according to the specific circumstances:
Kinematic: If we find an object moving through space on an elliptical course, then another object’s gravitation forced it to do so. If no other object is visible, we can venture to guess it is a black hole. Its mass can then be calculated based on the trajectory and the mass of the orbiting body.
Eruptive: If a star gets too close to a black hole, it might be totally destroyed under the right circumstances, which astronomers can observe in the form of X-ray and gamma-ray bursts, among other things. If there is no other possible cause, it must be a black hole.
Accretive: As described above, gas and dust in the vicinity of a black hole form a disk which radiates in the entire spectrum and is therefore visible.
Spectro-relativistic: If a star is near a black hole, its spectrum is distorted by gravitational effects, and this can be measured.
Obscurative: Near strong gravitational forces, especially around the edge of a black hole, the wavelength of lights is shifted toward red. The ring around the object therefore becomes brownish to black. Currently our telescopes are not strong enough to detect this, but it should be possible in the future, at first by primarily using radio telescopes.
Aberrative: Another effect of gravitation is that it bends light rays coming from objects behind the black hole. The hole thus becomes a lens. This gravitational lens effect can already be used today to find stellar black holes. This requires, though, that another luminous object is located behind the black hole along our line of sight.
Temporal: According to the theory of special relativity, effects occur in the immediate vicinity of black holes, particularly time dilation. Therefore, temporal sequences change, which can be detected if one knows the normal sequence in a ‘rest frame.’
Auditory: If a stone falls into water, concentric waves spread. The collision of a black hole with another one also generates waves—within space-time. They are called gravitational waves and have already been found several times with the help of the LIGO detector. In order to determine the precise location of the event, other analytical methods are usually needed as well.
The Information Paradox
In the first section you already learned that black holes have three specific properties: mass, angular momentum, and charge. This fact is known as the ‘no-hair theorem’ or ‘bald head theorem’: If you’ve seen one bald head, you’ve seen them all, since there is nothing else to be seen. But, what would happen to the information contained in matter if a particle disappeared into a black hole, never to be seen again? Similar laws of conservation apply to information as to matter, and the black hole seems to violate them. This is known as the ‘information paradox.’
At first it was believed that the concept of Hawking radiation would offer a way out. Couldn’t it contain the lost information? But that is not the case. The radiation only depends on the size of the hole, its mass.
There is no generally accepted solution for this paradox. Stephen Hawking thought black holes might have hairs under certain conditions, though other physicists reject this idea.
Another suggested solution is the concept of wormholes. In theory, a wormhole would spit out the information elsewhere, so to speak, so information would be gone but not lost. So far none have been detected, though, and they appear to be unlikely for other reasons.
The fact that black holes have limited lifespans is not the real problem for physicists. The really interesting question is, what happens to the information that ended up in a black hole—information that is theoretically indestructible? Even a black hole the size of the sun would last about 1067
years before it would be extinguished. If a black hole were immortal, physicists could take solace in the idea that information which crossed the event horizon might be forever lost from this side, but might still exists around the singularity. In order to resolve this paradox the physicists might need a so-called ‘theory of everything.’ Until that has been developed, they will have to make do with one of these independent scenarios:
The information is irretrievably lost. Unfortunately this conclusion violates the principle of the conservation of information. On the other hand, the mathematician Roger Penrose assumes in his cosmology a destruction of information inside a black hole.
Black holes are information-incontinent. They constantly leak information. Alas, this runs counter to current calculations for macroscopic black holes, which align well with reality.
When the black hole dies, all of the collected information escapes at once. This scenario is in accordance with current physics—except for the moment shortly before its violent death. In that instance a very, very small black hole would have to contain enormous amounts of information, which contradicts what we currently know about the maximum information density.
The final stage of a black hole is not greater than the shortest length in the universe, the ‘Planck length.’ It contains all information ever collected. Then physicists would not have to think of a way for the information to escape, as they have to do in scenario 3. On the other hand, the information density would be infinite, which is impossible.
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