# Black hole thermodynamics in the Sharma-Mittal generalized entropy formalism

## TL;DR

This paper explores the thermodynamic properties of Schwarzschild and Schwarzschild-de Sitter black holes using Sharma-Mittal entropy, revealing stability conditions and parameter relations through classical and semi-classical analyses.

## Contribution

It introduces the application of Sharma-Mittal entropy to black hole thermodynamics, providing new insights into stability and entropy parameter relations.

## Key findings

- Schwarzschild black hole is always stable in the micro-canonical ensemble.
- Stability in the canonical ensemble depends on black hole mass.
- Semi-classical analysis yields approximate relations between entropy parameters.

## Abstract

Using the Sharma-Mittal entropy, we study some properties of the Schwarzschild and Schwarzschild-de Sitter black holes. The results are compared with those obtained by attributing the Bekenstein entropy bound to the mentioned black holes. Our main results show that while the Schwarzschild black hole is always stable in the micro-canonical ensemble, it can be stable in the canonical ensemble if its mass is bigger than the mass of the coldest Schwarzschild black hole. A semi-classical analysis has also been used to find an approximate relation between the entropy free parameters. Throughout the paper, we use units $c=G=\hbar=k_B=1$, where $k_B$ denotes the Boltzmann constant.