Monday, February 18, 2013

Degenerate Matter: Black Holes

This post concerns black holes in the context of degenerate matter. For an introduction to degenerate matter, followed by a description the various stages of a stellar remnant's collapse preceding the possible formation of a black hole, see here.

White dwarfs, neutron stars, and hypothetical exotic stars are examples of objects of various masses within which some force counteracts gravity and stops collapsed stellar cores from shrinking further. However, above about 3.5-4 solar masses, no known force can counteract gravity. The collapsed star shrinks even further, until its escape velocity, the velocity necessary to leave the object from its surface, reaches the speed of light. At this stage, nothing can escape the body, not even the fastest particles in the Universe: photons. The collapsed star has become a black hole.

As far as is known, no further phenomenon can halt the contraction of the stellar remnant. Under its own weight, the black hole would collapse to become infinitely small and infinitely dense: such an object is called a singularity. Such singularities are consistent with the theory of relativity, but it is not known whether a singularity would be compatible with quantum mechanics; an infinitely dense object seems contrary to any known particle behavior.

Despite the complexities of black hole formation, the structure of a black hole is very simple. In some ways, as we shall see, it is even too simple. From long distances away, a black hole exerts gravity just the same as any other object. For example, light near a black hole undergoes gravitational lensing just as light around neutron stars does (see below).

The above is an impression (not a real image) of gravitational lensing. The gravity of a black hole is so great that it bends light, and therefore causes the view of objects behind the black hole to be distorted.

Near to the black hole, the only noticeable features are the accretion disk and the event horizon. The accretion disk is simply infalling material, sucked in by the black hole's gravity. Such matter is often accelerated to enormous speeds, and releases high energy radiation (X-rays and gamma rays) before it falls into the black hole. This is why black holes can be detected, as no radiation (with a possible exception, see below) is emitted from the hole itself.

The event horizon, which is the real "edge" of the black hole, is the boundary beyond which the velocity needed to escape the black hole exceeds the speed of light. At the center of the area bounded by the event horizon is the actual stellar remnant, the composition of which, as remarked above, is unknown.

The formation of a black hole has been discussed, but do these objects ever die? In fact, they are predicted to "evaporate" by emitting Hawking radiation, named after the physicist Stephen Hawking, who first proposed the process in 1974. Though no particles can escape a black hole, certain fluctuations of space can spontaneously create particle-antiparticle pairs near the event horizon. When this happens, one of the particles can escape by a process known as quantum tunneling. The precise nature of this radiation is unknown, but the rate of emission is so slow that the background radiation of the Universe gives more energy to most black holes than they lose through Hawking radiation. However, the amount of radiation emitted is inversely proportional to a black hole's size, so a small black hole (below stellar mass) could evaporate in our current Universe, if one existed. Black holes that are stellar remnants, however, will remain in existence for trillions of years, as the cosmic background radiation is still energetic enough to insure that they take in more mass then they give off. If the Universe's expansion continues, black holes are likely to be the last large objects in the Universe in the very far future (perhaps about 1040 years from now).

The characteristics of a black hole are its mass, spin (or angular momentum), and electric charge. The latter two of these yield interesting phenomena. When a black hole is spinning, it provides angular momentum to the matter circling it, giving rise to a special region called the ergosphere (see below).

The ergosphere is a region outside the event horizon. Any matter in this region is subjected to not only the gravity of the black hole but also the drag of spacetime itself resulting from the angular momentum of the black hole. Therefore, even though the escape velocity in the region is lower than the speed of light, the sum of this and the additional momentum causes any matter in the region to be moved in the direction of rotation of the black hole. This occurs in such a way that a particle in the ergosphere would have to move at superliminal (over the speed of light) speeds to stay stationary (with respect to an outside frame of reference).

With regard to the electric charge of a black hole, some theories of the universe, notably string theory, acknowledge the possibility of the existence of what is called a magnetic monopole, essentially analogous to "a bar magnet with only one end". Even particles such as electrons, though possessing a net electric charge, have, due to their spin, a typical magnetic dipole called a magnetic moment, which obeys the laws of magnetism. A monopole would have to be composed of some unknown particle, as all elementary particles known to date have magnetic dipole moments. Black holes may be composed of these monopoles, as they are likely to be made of some other elementary particle. Note that these ideas are quantum mechanical. If black holes are true singularities, it may preclude this possibility.

The above are a few exotic phenomena that can arise in black holes. However, returning to the characteristics of the black hole, the three listed above are the only ones known that can be calculated by an outside observer, i.e. by the black hole's effect on its environment. From this viewpoint, one could precisely determine the nature of a black hole with only three parameters. Yet, if an object, say an apple, were to fall into a black hole, there would be no way of knowing afterward that this had occurred! One could record the mass contribution of the apple to the hole, but there is no way of recovering its shape, its color, etc., from observation of the black hole. The information that the apple carried is lost.

Or is it? Many principles of physics are contrary to this assumption. Classical physics and relativity both imply reversibility, that is, they imply that a "simulation" of the universe could be run just as well forward in time or backward. The amount of information in the universe must remain constant, or, in running time backward, one could have no idea of whether an apple, an orange, or any other object of equivalent mass had fallen into the black hole. Furthermore, an important quantum mechanical equation, the wave equation, totally determines of the probabilities of quantum states at any past or future time given the wave equation of a system at the present time. Therefore there can be no "collapse" of many states into one; the scenario with the apple and that with the orange cannot have the same outcome.

Many resolutions to this paradox have been posited. Some state that the information would be conserved in some (initially) non-observable fashion: the information would "leak out" slowly over time as black holes Hawking radiation, or that black holes, at the end of their life, would release all their stored information in a single burst, or even that the information is transported, by means of the singularity through a hole in spacetime, to another universe. However, all three of these violate some aspect of our current understanding of information conservation.

If information leaks out, there is still a time delay in which it is not known. It seems unlikely that all of the information is emitted at the end of a black hole's lifetime, as many theories put a limit on the amount of information that can be stored in a finite volume of space. Finally, if the information is transported to another Universe, the information is not conserved in any local, or obtainable, sense. There is a final alternative, however. It is possible that the fluctuations of the event horizon itself would store the impressions of the incoming (or outgoing) particles. Note that this requires the projection of the information in a four-dimensional space (three spatial dimensions plus time) onto a three-dimensional space (the surface of the event horizon is a two-dimensional surface, which again changes over time), but this poses no problem, and has sound mathematical justification; for a sufficiently "well-behaved function" on a space, the behavior of the function within a region is completely determined by the values of the function on its boundary. This result is known as Green's theorem, and its application to the projection of information onto the event horizon is known as the holographic principle.

Of course, this does not mean we could practically access this information, but simply states that it is, in theory, possible. Other obstacles prevent one from ever reaching the event horizon. One notable phenomenon is relativistic time dilation.

Any massive object creates a depression in space, and a black hole creates an especially steep depression; in fact, if singularities exist as predicted by relativity, the depression would actually be a hole in space, as illustrated above. Due to the symmetry between time and space, again predicted by relativity, time is accordingly distorted near a black hole. If one were to watch another object, or person, approach the event horizon, they would appear to slow down as they neared the edge of the black hole. In fact, from the perspective of an outside observer, they would take infinitely long to cross the horizon itself. From the viewpoint of the object, however, time does not slow, and the crossing of the horizon takes place in finite time.

Of course, no object could actually survive this crossing, but would rather be torn apart by gravitational pull. In addition, no one could actually watch the entire descent, as the radiation that renders one visible, when travelling from the object to the observer, uses energy to move "uphill" in the black hole's gravity field. Lower energy light, for example, is red, so the radiation is said to have red-shifted. By the time an object is close to the horizon, it is only visible in radio waves, and eventually, not at all.

The key concept of degenerate matter is the interplay between gravitation and quantum mechanical forces, in particular how they oppose one another. Black holes, the culmination of the process of stellar collapse, represent the crux of the differences between "large-scale" physical theories, i.e. relativity, and "small-scale" theories, i.e. quantum mechanics. Singularities are present in relativity as "pathological" points in spacetime, where density becomes infinite. However, in light of quantum mechanics, singularities are seem to be contradiction, resulting in exotic phenomena including, but not limited to, those listed above.

Solving the mysteries of degenerate matter and black holes in particular is one of the main outstanding problem in modern physics, and will continue to shape our understanding of the universe for years to come.

Sources:, No-hair theorem on Wikipedia

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