# Analysis of black hole thermodynamics under Generalized uncertainty principle from the doubly special relativity

## TL;DR

This paper explores how the generalized uncertainty principle within doubly special relativity modifies the thermodynamic properties of topological charged black holes in AdS space, revealing new insights into black hole physics.

## Contribution

It introduces a novel analysis of black hole thermodynamics incorporating GUP and DSR, providing both heuristic and analytical results and comparing their effects.

## Key findings

- Thermodynamic properties like temperature, entropy, and heat capacity are modified under DSR-GUP.
- The study shows how black hole characteristics influence thermodynamics under different conditions.
- Analytical and heuristic approaches yield consistent results, enhancing understanding of quantum gravity effects.

## Abstract

In this paper, we investigate effect of the generalized uncertainty principle (GUP) under the doubly special relativity (DSR) on the thermodynamics properties of the topological charged black hole in Anti-de Sitter (AdS) space only in the spherical horizon case have. Our study is based on a heuristic analysis of a particle which is captured by the black hole. We also report here some results of a usual analytical computation. However, we obtain the black hole thermodynamic properties as familiar concepts such as temperature, entropy and heat capacity under DSR-GUP. we also compare our both analytical results. Beside we discuss the behavior of the corrected thermodynamic properties vs. changes of black hole characteristics under different condition.