Once Before Time - Martin Bojowald [111]
QUANTUM GRAVITY OF BLACK HOLES: LIFE MUST GO ON
If black holes emit energy, they can be considered to be analogs of the excited atoms that tell us much about the discrete energies in quantum mechanics. Atoms in an energetic state above the ground state can emit surplus energy to transit to the ground state. Possible amounts of radiation energy, measured in the atom’s emission spectrum, provide insights into atomic structures in quantum mechanics. Black holes, similarly, are gravitationally bound systems whose radiation can give hints about their structure. They emit energy by the Hawking process, as yet unmeasured but computed. In studying Hawking radiation, one makes use of general relativity and the quantum theory of matter, and one obtains a result not fully consistent within those theories as a result of the information loss problem. In particular, the end state after Hawking evaporation cannot be understood in this way. The final state indeed looks analogous to the atomic ground state, to be described only by means of a complete quantum mechanics. To understand the finale of Hawking radiation, a quantum theory of gravitation, space, and time is needed—not one of matter alone as in Hawking’s calculations.
String theory has difficulties with the dense regions around the singularity, because of the lack of a detailed understanding of space-time structure, and has not provided a concrete picture for what black holes might look like in quantum gravity. Rather, it tackles such questions by looking at the singularity from a safe distance, in fact from infinitely far away: It provides so-called holographic descriptions in which everything that is going on somewhere in space-time is represented by structures at the edge of space-time out at infinity. (Similarly, a hologram presents a three-dimensional scene on a two-dimensional screen.) Mathematically, this process is elegant, but it is also indirect and not very concrete. With these constructions, string theorists have vaguely concluded that no information is lost in a black hole since the screen infinitely far away does not lose information. But the question remains whether the description by the screen is complete; if it is not, information in the full state may still be lost.
String theory models have been more successful for a description of the horizon than of the singularity of a black hole. Although the horizon is not a material surface, it should have a microscopic structure owing to the atomic nature of space and time. One can then try to count the number of building blocks, or the number of all possible ways to construct a black hole of a certain size. As undertaken by Andrew Strominger and Cumrun Vafa, one can count all possible states (the so-called black hole entropy) in string theory. Such calculations are often seen as the first test that any quantum theory of gravity must pass, and they have been performed successfully in string theory at least for certain types of highly charged black holes. These objects are not quite realistic, for a charged matter distribution under collapse would eject charged particles and be almost neutral once a black hole forms; nevertheless, the successful calculations in string theory present an important consistency result. This encouraging outcome is, however, no proof that the theory is correct, and it does not necessarily distinguish it from others. Loop quantum gravity, too, shortly after string theory, succeeded, by a rather different calculation, in deriving and analyzing black hole entropy—and that for a much more realistic class of uncharged black holes.6