Effective temperature, Hawking radiation and quasinormal modes

TL;DR

This paper introduces an effective temperature approach to analyze black hole quasinormal modes, revealing modifications to area quantization, entropy, and microstates, thus impacting the understanding of black hole quantum physics.

Contribution

It presents a novel analysis of black hole quasinormal modes using an effective temperature, altering key quantum gravity results and their dependence on overtone numbers.

Findings

Modified horizon area quantization formulas

Entropy and microstates depend on overtone number n

Reproduction of previous results in the large n limit

Abstract

Parikh and Wilczek have shown that Hawking radiation's spectrum cannot be strictly thermal. Such a non-strictly thermal character implies that the spectrum is also not strictly continuous and thus generates a natural correspondence between Hawking radiation and black hole's quasinormal modes. This issue endorses the idea that, in an underlying unitary quantum gravity theory, black holes result highly excited states. We use this key point to re-analyze the spectrum of black hole's quasinormal modes by introducing a black hole's effective temperature. Our analysis changes the physical understanding of such a spectrum and enables a re-examination of various results in the literature which realizes important modifies on quantum physics of black holes. In particular, the formula of the horizon's area quantization and the number of quanta of area are modified becoming functions of the quantum "overtone" number n. Consequently, Bekenstein-Hawking entropy, its sub-leading corrections and the number of microstates, i.e. quantities which are fundamental to realize unitary quantum gravity theory, are also modified. They become functions of the quantum overtone number too. Previous results in the literature are re-obtained in the very large n limit.