# Thermodynamic studies of Different Type of Black Holes: General Uncertainty Principle Approach

## TL;DR

This paper investigates the thermodynamics of Kiselev and Taub-NUT black holes, incorporating quantum corrections via the General Uncertainty Principle, and analyzes their stability, emission rates, and phase transitions.

## Contribution

It introduces quantum-corrected thermodynamics for different black holes using the General Uncertainty Principle, including stability and phase transition analysis.

## Key findings

- Black holes exhibit phase transitions in their thermodynamic behavior.
- Quantum corrections introduce logarithmic terms in entropy.
- Thermal stability varies with black hole parameters and quantum effects.

## Abstract

We present an investigation on thermodynamics of two different types of black holes viz. Kiselev black hole (asymptotically flat) and Taub-NUT (non-asymptotically flat) black hole. We compute the thermodynamic variables like black hole's Hawking temperature, entropy at the black hole's event horizon. Further we derive the heat capacity and examine it to study the thermal stability of the black holes. We also calculate the rate of emission assuming the black holes radiate energy in terms of photons by tunneling. We represent all the parameters including the rate of emission of the black holes graphically and interpret them physically. We depict a comparative study of thermodynamics between the afroesaid types of black holes. Here we find the existence of a transition of phase. Finally, we obtain the quantum-corrected thermodynamics on the basis of general uncertainty principle and it is seen from the quantum-corrected entropy that it contains the logarithmic term. We offer comparative studies on joint effect of generalised uncertainty principle parameter $\alpha$ along with the concerned black holes' parameters on the thermodynamics.