The semi-classical stress-energy tensor in a Schwarzschild background, the information paradox, and the fate of an evaporating black hole

Abstract

Analytic approximations to and numerical results for the semi-classical stress-energy tensor outside the horizon of a Schwarzschild black hole obtained in the 1980's and 1990's are re-examined in order to better understand the origin of Hawking radiation and the implications for the black hole information paradox. Polynomial fits to the numerical results for the tangential stress in 4D are obtained for conformally coupled spin 0 and spin 1 fields in the Hartle-Hawking and Unruh quantum states. What these results show is that the origin of the Hawking radiation is not pair creation or tunneling very close to the black hole horizon, but rather is a nonlocal process extending beyond the potential barrier in the mode propagation equations centered around $r=3M$. Arguments are presented that the black hole information paradox cannot plausibly be addressed by processes occurring close to the horizon of a black hole whose geometry is close to Schwarzschild. However, a toy model for the evolution of the black hole geometry based on the Bousso covariant entropy bound suggests a possible resolution.

arXiv comment35 pages, 10 figures

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• The Return of the Singularities: Applications of the Smeared Null Energy Condition
• Schwarzschild Fuzzball and Explicitly Unitary Hawking Radiations
• Models for the nonsingular transition of an evaporating black hole into a white hole
• Interpreting the semi-classical stress-energy tensor in a Schwarzschild background, implications for the information paradox
• Information Missing Puzzle, Where Is Hawking's Error?
• Black holes to white holes I. A complete quasi-classical model