Once Before Time - Martin Bojowald [115]
Homogeneity significantly simplifies investigating the dynamics, since all places in space can be considered at once. Just one equation, as on this page, is to be solved for the whole interior, instead of uncounted numbers for all the spatial atoms. We already know the result from quantum cosmology: The singularity of the classical theory is traversed without the disintegration of space. For a black hole, this means that its interior must open up to the exterior after the horizon evaporates, and thus will become visible for an observer.
Incomplete knowledge of quantum gravity notwithstanding, there is a unique prediction. One must keep in mind, though, that we had to use different assumptions and indications in this chain of proofs, still to be buttressed by detailed calculations or even the redelivery of missing theoretical elements. The most important step will be to solder the interior dynamics, for which we used cosmological results, to the so far poorly understood exterior dynamics. We started our argumentation with the required completeness of an encompassing theory, according to which the homogeneous interior dynamics can consistently be combined with the exterior dynamics describing the horizon’s evaporation. The picture as described may thus be taken as a prediction of current ingredients of the theory, whose consistency can be further substantiated once extended calculations become available. If this process is successful, the result should also be generalizable to rotating black holes, where our present arguments lose their validity as a result of the inhomogeneous interior in this case.
The lucky relation of the nonrotating black hole interior to cosmological equations also allows the development of a preliminary but concrete picture of the black hole and its fate after evaporation. Again, the existence of a repulsive force is crucial, as it arises at high compressions of the collapsed matter when quantum gravity is considered. Matter, then, cannot collapse completely to the point in time of the classical singularity; it is instead being dispersed out after sufficiently strong compression. As in cosmology, the limited storage space of discrete time is responsible for the emergence of this counterforce. Maximal compression is obtained in the black hole’s center, allowing the singularity in general relativity but not in quantum gravity. Seen from outside, this point in time is marked by the horizon’s disappearance by evaporation. As illustrated in figure 29, the interior, in contrast to the classical scenario, will again be visible from the outside in the form of hot, extremely dense matter, driven apart by the repulsive forces of quantum gravity as in a mini-bang. From the outside, one would first see the rest of the Hawking radiation, soon overpowered by the exploding interior’s glare.
29. Representation of astronomical observations at a nonsingular black hole. Moving in time along the top right border, we first encounter radiation that had passed the black hole before it formed (bottom arrow). As the first signal from the black hole, one sees Hawking radiation