On the temperature of the quantum black hole

TL;DR

This paper investigates the temperature of quantum black holes, addressing a discrepancy in Hawking temperature calculations by proposing a generalized thermofield double state to resolve the factor of two correction.

Contribution

It introduces a generalized thermofield double framework to correct the Hawking temperature discrepancy in quantum black holes.

Findings

The factor of two correction in Hawking temperature can be fixed.

A generalized thermofield double state aligns the temperature with the Bekenstein-Hawking entropy.

The approach offers new insights into black hole thermodynamics and quantum states.

Abstract

A nontrivial peculiarity of general relativity is that when the horizon region of black holes is rendered harmless, the exterior doubles, resulting in a causally disconnected parallel universe. This intricacy plays a central role in 't Hooft's unitarity arguments, emphasising an exact identification between the physical universe and its duplicate on the other side of the horizon. However, it leads to another tension in the form of a factor of two correction in Hawking's temperature. This discrepancy is concerning because the Rindler temperature is universal and complies with the Bekenstein-Hawking entropy. We demonstrate that the mismatch in the Boltzmann factor gets fixed if the state that forms the corresponding density matrix adopts a generalised thermofield double structure. That leaves room for some interesting discussion.