Once Before Time - Martin Bojowald [112]
More interesting, but also more complicated, than the number of states for a fixed-size black hole is its behavior when it exchanges energy with its surroundings—either by absorbing more matter or by emitting Hawking radiation. In the discrete picture of loop quantum gravity, black holes present a kind of atomic system built not from blocks of matter but from chunks of quantized space-time. A Hawking photon is emitted when the black hole changes its state of energy or mass. Hawking radiation is described by a theory of waves in a given space-time, similar to Planck’s formula for the radiation in a black box. To understand the emergence of this radiation better, one must add a theory of the walls of the box and their interaction with the radiation by emission and absorption of photons. For the box, Einstein had achieved a successful theory of emission and absorption by his explanation of Planck’s formula.
For a black hole, one needs a quantum theory of space-time near the horizon because that is where the Hawking particles are generated. A final explanation must use quantum gravity. Once the explanation is available, one can perform spectroscopy of black holes analogous to that of atoms and molecules, which was so important when quantum mechanics was developed. What will remain out of reach for a long time, however, is a comparison with observations, for they would have to measure not just Hawking radiation itself but also its details such as the intensity distribution over different wavelengths. For astrophysical black holes, our universe, despite all its expansion and dilution, is simply still too warm, dwarfing Hawking radiation by the cosmic microwave background.
Still, even theoretical spectroscopy allows many interesting questions. The atomic structure of space and time, as it arises in loop quantum gravity, indicates that the surface area and the mass of black holes, related to each other by the Schwarzschild radius, can take only discrete values. Based on general principles, this was postulated by Jacob Bekenstein shortly before Hawking’s calculations. Loop quantum gravity by now presents a concrete proposal for the mathematical form of the discrete sizes constructible by stacking together atoms of space. But one still has to see which transitions happen when Hawking radiation arises, or how atoms of space are transformed into radiation particles. Of particular interest is the question of whether a black hole has a ground state akin to that of an atom, and what space-time could represent this state. At the end of the Hawking process one should, by the atom analogy, expect the black hole to be in the state of lowest energy; its form is thus decisive for the question of whether Hawking evaporation indeed destroys all information, or whether there is a compact core for storage.
Then again, the analogy to atoms may in the end lead to wrong conclusions even though it can describe the first steps of Hawking evaporation. For as the black hole becomes smaller and smaller, the Hawking emitting horizon approaches the singularity and its high-curvature region ever more closely. Nothing comparable happens in material atoms, where instead energy simply decreases when an atom approaches the ground state. In the ground state, properties of quantum theory are very important, for otherwise the classical stability problem could not have been solved; but no phenomenon of high energy density, as the singularity presents it, arises. To answer the crucial questions about black holes, the singularity and its fate in quantum gravity must be understood.
As in cosmology, there are two components of loop quantum gravity that can make the singularity disappear: repulsive forces, and the availability of more time by time’s discretization. With black holes, we cannot rely on such symmetrical situations as in cosmology, because homogeneity would be too strong: We require a distinct point as the center of rotational symmetry, and the gravitational force changes with the distance from that point. Calculations are more complex, and the possibilities