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

TL;DR

This paper investigates semiclassical corrections to the entropy of the (2+1) BTZ black hole caused by self-gravitation effects during Hawking radiation, finding negative corrections proportional to the horizon area.

Contribution

It provides a first-order semiclassical correction to the Bekenstein-Hawking entropy for the BTZ black hole considering self-gravitation effects as a tunnelling process.

Findings

Corrections to entropy are negative.

Modified entropy is proportional to the horizon.

First-order correction factor is evaluated.

Abstract

Hawking radiation is viewed as a tunnelling process. In this way the effect of self-gravitation gives rise to semiclassical 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. In this semiclassical analysis, corrections to the Bekenstein-Hawking formula $S_{BH}=\mathcal{A}_{H} / 4l_{P}^{2}$ are found to be negative and the proportionality factor connecting the modified entropy, $S_{bh}$, of the (2+1) BTZ black hole to the Bekenstein-Hawking entropy, $S_{BH}$, is evaluated to first order in $\omega$.