Semiclassical corrections to the Bekenstein–Hawking entropy of the BTZ black hole via self-gravitation

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 ω 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 SBH=AH/4lP2 are found to be negative and the proportionality factor connecting the modified entropy, Sbh, of the (2+1) BTZ black hole to the Bekenstein–Hawking entropy, SBH, is evaluated to first order in ω.