Relativistic Correction to Black Hole Entropy

TL;DR

This paper investigates how relativistic effects modify the entropy of black holes, specifically in non-rotating BTZ and AdS-Schwarzschild cases, highlighting the significance of these corrections at high temperatures.

Contribution

It generalizes entropy calculations using relativistic Kaniadakis statistics, revealing logarithmic corrections and their importance in high-temperature regimes.

Findings

Relativistic corrections to black hole entropy are logarithmic.

Corrections become significant at high temperatures.

Non-relativistic limit recovered as $pparightarrow 0$.

Abstract

In this paper, we study the relativistic correction to Bekenstein-Hawking entropy in the canonical ensemble and isothermal-isobaric ensemble and apply it to the cases of non-rotating BTZ and AdS-Schwarzschild black holes. This is realized by generalizing the equations obtained using Boltzmann-Gibbs(BG) statistics with its relativistic generalization, Kaniadakis statistics, or $\kappa$-statistics. The relativistic corrections are found to be logarithmic in nature and it is observed that their effect becomes appreciable in the high-temperature limit suggesting that the entropy corrections must include these relativistically corrected terms while taking the aforementioned limit. The non-relativistic corrections are recovered in the $\kappa\rightarrow 0$ limit.