# Thermodynamics of Reissner-Nordstr\"om Black Holes in Higher Dimensions: Rainbow Gravity Background With General Uncertainty Principle

## TL;DR

This paper explores the thermodynamics of higher-dimensional Reissner-Nordstr"om black holes within rainbow gravity and generalized uncertainty principle frameworks, revealing remnant masses, phase transitions, and stability characteristics through graphical and analytical methods.

## Contribution

It introduces a comprehensive analysis of black hole thermodynamics incorporating rainbow gravity and GUP effects across multiple dimensions, highlighting new phase transition behaviors and stability conditions.

## Key findings

- Existence of black hole remnants and critical masses.
- Presence of phase transitions in all dimensions.
- Differing phase transition behaviors observed by local and horizon measurements.

## Abstract

In this paper, we investigate the thermodynamic properties of Reissner-Nordstr\"om black holes embedded in higher $(d)$ dimensions in the framework of rainbow gravity incorporating the effects of the generalized uncertainty principle. We also examine all the properties graphically by varying the rainbow gravity parameter $\eta$ and the generalized uncertainty principle parameter $\alpha$. We find the existence of remnant and critical mass of the concerned black hole. We calculate the local temperature, local internal energy and hence we analyse the thermal stability of the black hole by computing the local heat capacity. Further, we study the phase transitions of the aforesaid black hole solution under the effects of generalized uncertainty principle. From the analysis of the specific heat at the horizon, we observe that there are phase transitions for all dimensions but when we analyze the same, measured by the local observer, we find that there exist only two phase transitions.