Back reaction, emission spectrum and entropy spectroscopy

TL;DR

This paper extends the reformulated tunneling framework to include back reaction effects, showing that the emission spectrum remains non-thermal and the entropy spectrum's quantum is unaffected, but it still cannot resolve the black hole information paradox.

Contribution

The study adapts the tunneling framework to incorporate back reaction effects, aligning with Parikh-Wilczek's findings and analyzing implications for black hole information.

Findings

Emission spectrum is non-thermal when back reaction is included.

Entropy quantum remains unchanged despite back reaction effects.

Tunneling formalism does not resolve the black hole information paradox.

Abstract

Recently, an interesting work, which reformulates the tunneling framework to directly produce the Hawking emission spectrum and entropy spectroscopy in the tunneling picture, has been received a broad attention. However, during the emission process, most related observations have not incorporated the effects of back reaction on the background spacetime, whose derivations are therefore not the desiring results for the real physical process. With this point as a central motivation, in this paper we suitably adapt the \emph{reformulated} tunneling framework so that it can well accommodate the effects of back reaction to produce the Hawking emission spectrum and entropy spectroscopy. Consequently, we interestingly find that, when back reaction is considered, the Parikh-Wilczek's outstanding observations that, an isolated radiating black hole has an unitary-evolving emission spectrum that is \emph{not} precisely thermal, but is related to the change of the Bekenstein-Hawking entropy, can also be reproduced in the reformulated tunneling framework, meanwhile the entropy spectrum has the same form as that without inclusion of back reaction, which demonstrates the entropy quantum is \emph{independent} of the effects of back reaction. As our final analysis, we concentrate on the issues of the black hole information, but \emph{unfortunately} find that, even including the effects of back reaction and higher-order quantum corrections, such tunneling formalism can still not provide a mechanism for preserving the black hole information.