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Semiclassical corrections to the Bekenstein-Hawking entropy of the BTZ black hole via self-gravitation. (English) Zbl 0994.83031
Summary: 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 \(S_{\text{BH}}=A_H/4l_P^2\) are found to be negative and the proportionality factor connecting the modified entropy, \(S_{\text{bh}}\), of the \((2+1)\) BTZ black hole to the Bekenstein-Hawking entropy, \(S_{\text{BH}}\), is evaluated to first order in \(\omega\).

MSC:
83C57 Black holes
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