New coordinates for BTZ black hole and Hawking radiation via tunnelling

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 Painlevé coordinate system (Painlevé–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.