# Thermodynamics of Higher Order Entropy Corrected Schwarzschild-Beltrami-de Sitter Black Hole

## TL;DR

This paper explores how higher order entropy corrections influence the thermodynamics of Schwarzschild-Beltrami-de Sitter black holes, revealing potential stability improvements and phase transitions due to thermal fluctuations.

## Contribution

It introduces higher order entropy corrections into the thermodynamics of a specific black hole solution, analyzing their effects on stability and phase transitions.

## Key findings

- Higher order corrections can remove black hole instabilities.
- Thermal fluctuations induce phase transitions.
- Presence of corrections affects thermodynamic laws.

## Abstract

In this paper, we consider higher order correction of the entropy and study the thermodynamical properties of recently proposed Schwarzschild-Beltrami-de Sitter black hole, which is indeed an exact solution of Einstein equation with a positive cosmological constant. By using the corrected entropy and Hawking temperature we extract some thermodynamical quantities like Gibbs and Helmholtz free energies and heat capacity. We also investigate the first and second laws of thermodynamics. We find that presence of higher order corrections, which come from thermal fluctuations, may remove some instabilities of the black hole. Also unstable to stable phase transition is possible in presence of the first and second order corrections.