Once Before Time - Martin Bojowald [109]
On the way to a quantum theory of black holes we first need more details about Hawking radiation. Its derivation does not rely on any version of quantum gravity; rather, it uses quantum effects of matter in a universe that is curved by space-time transformations but is not quantum itself. Even here, as during inflation, the special, trembling form of space-time causes particles to be created from the vacuum. As seen in figure 23, the diagram of a black hole has a form entirely different from that of other astrophysical objects in figure 22 or of empty space in figure 21. Differences are noticeable especially at the horizon and beyond, in the black hole interior; near the horizon we have a very different structure of space-time than at safe distance from it.
As in the analogy of the seabed’s influencing the propagation of waves in quantum theory, or in the example of inflationary generation of matter from the vacuum in cosmology, the form of space-time is responsible for the behavior of a quantum mechanical wave function of matter. Wave functions of matter are influenced by the unsteady ground of space-time near the horizon such that partial waves with particle character split off. In the particle picture, this happens through the creation of particle-antiparticle pairs, one partner falling into the black hole, the other one escaping as part of Hawking radiation.
With the escaping particles, the black hole loses energy and mass. Its horizon, with a radius proportional to the mass, shrinks. Initially, all this happens extremely slowly because the temperature of a heavy black hole is very low and not much energy is emitted. A large black hole has a horizon far away from the singularity; near the horizon, deviations of space-time from that in empty space are realized in a much smaller fashion than for lighter black holes. In the seabed picture, the ground near the large horizon of a heavy black hole is more similar to empty space than that around the small horizon of a lighter black hole; fewer waves, or particles, are being created.
Unless more energy from the outside happens to fall in than is radiated away by the Hawking effect, the horizon radius must continue to shrink. For black holes in the usual mass range, such as can be found in the universe, even the weak cosmic background radiation right now provides enough energy to stabilize black holes against Hawking evaporation. With further expansion of the universe, however, the background radiation will cool down more and become ever weaker. Lighter black holes will start to evaporate sometime in the distant future. Only engulfing neighboring matter such as stars or intergalactic gas can save them from evaporation, but this food will eventually be used up. Viewed over the whole history of the universe, the case of evaporating black holes is thus rather realistic.
When it starts to evaporate, a black hole shrinks and heats up more and more. This enhances the evaporation process and must, if it is simply extrapolated, lead to the disappearance of the horizon after some finite time. Such a theoretical extrapolation, however, is not valid, because the horizon, once small, eventually comes close to the singularity in the strong curvature region. At this stage one needs a quantum theory of gravity, which Hawking did not take into account. His calculations were instead based on general relativity describing the black hole and its horizon, and on the quantum theory of matter in this space-time—but not on that of space-time itself.
On its own, the Hawking process cannot help in the decision as to what the black hole singularity really means. The singularity does not simply disappear into thin air (or faint radiation); the quantum theory of matter alone cannot provide a solution to the singularity problem. Instead, the evaporation reveals further problems with the classical picture, which are useful in stimulating a later resolution in quantum gravity by providing different viewpoints.
Most widely discussed among these problems