Quantum Corrections to the Bekenstein-Hawking entropy of the BTZ Black Hole via Self-Gravitation

Abstract

Hawking radiation is viewed as a tunnelling process. In this way the effect of self-gravitation gives rise to quantum corrections to the entropy of the (2+1) BTZ black hole. The modified entropy, due to specific modelling of the self-gravitation effect, of the (2+1) BTZ black hole is evaluated. To first order in $\omega$ which is a shell of energy radiated outwards the event horizon of the BTZ black hole, modified entropy is proportional to the horizon. Quantum corrections to the Bekenstein-Hawking formula $S_{BH}=\mathcal{A}_{H} / 4l_{P}^{2}$ are found to be negative. In this semiclassical analysis the Immirzi parameter appears and is evaluated to first order in $\omega$.