New Coordinates for BTZ Black Hole and Hawking Radiation via Tunnelling

TL;DR

This paper introduces a new coordinate system for the BTZ black hole to analyze Hawking radiation as a tunnelling process, showing that the radiation spectrum is non-thermal and consistent with unitarity, with implications for black hole entropy.

Contribution

The paper develops a generalized Painleve coordinate system for BTZ black holes to study tunnelling Hawking radiation, revealing non-thermal spectra and entropy considerations.

Findings

Radiation spectrum is non-thermal

Coordinate choice affects entropy correction

Results align with unitarity principles

Abstract

Hawking radiation can usefully be viewed as a semi-classical tunnelling process that originates at the black hole horizon. For the stationary axisymmetric BTZ black hole, a generalized Painleve coordinate system (Painleve-BTZ coordinates) is introduced, and Hawking radiation as tunnelling under the effect of self-gravitation is investigated. The corrected radiation is obtained which is not precise thermal spectrum. The result is consistent with the underlying unitary theory. Moreover, Bekenstein-Hawking entropy of BTZ black hole is not necessarily corrected when we choose appropriate coordinate system to study the tunnelling effect.