On the paradox of Hawking radiation in a maximally extended Schwarzschild solution

Abstract

This paper considers the effect of Hawking radiation on an eternal black hole - that is. a maximally extended Schwarzschild solution. Symmetry considerations that hold independent of the details of the emission mechanism show there is an inconsistency in the claim that such a blackhole evaporates away in a finite time. In essence: because the external domain is static, there is an infinite time available for the process to take place, so whenever the evaporation process is claimed to come to completion, it should have happened earlier. The problem is identified to lie in the claim that the locus of emission of Hawking radiation lies just outside the globally defined event horizon. Rather, the emission domain must be mainly located inside the event horizon, so most of the Hawking radiation ends up at this singularity rather than at infinity and the black hole never evaporates away. This result supports a previous claim [arXiv:1310.4771] that astrophysical black holes do not evaporate.