Evaluation of physical properties of Kiselev like AdS spacetime in the context of $f(R,~T)$ gravity under the impact of quantum gravity

TL;DR

This paper investigates the effects of $f(R,T)$ gravity, quantum gravity, and particle kinetics on the thermodynamics of Kiselev-like AdS black holes, deriving modifications to Hawking temperature and entropy corrections.

Contribution

It introduces a detailed analysis of Hawking temperature and entropy in Kiselev-like AdS black holes within $f(R,T)$ gravity considering quantum gravity effects and particle kinetics.

Findings

Derived modified Hawking temperature in $f(R,T)$ gravity with quantum effects.

Calculated entropy corrections due to quantum gravity and particle kinetics.

Analyzed the impact of $f(R,T)$ gravity parameters on black hole thermodynamics.

Abstract

The developments of the $f(R,~T)$ gravity theory, which is a logical expansion of general relativity according to Einstein, inspire us to examine this theory in greater detail and take up our study to obtain a modification of the Kiselev-like AdS black holes scenario. In this study, we employ the semi-classical Hamilton-Jacobi procedure to investigate the Hawking temperature $(T_{H})$ for 4-dimensional Kiselev-like AdS BHs in the context of $f(R,~T)$ gravity. We derive the temperature using a standard formula for Kiselev-like AdS BHs in the context of $f(R,~T)$ gravity. The relativistic field equation in the context of the generalized uncertainty principle (GUP), the semi-classical Hamilton-Jacobi procedure, and the WKB strategy are used to tunnel boson particles into the horizon under the effect of quantum gravity as well as Hawking temperature and also use this temperature to compute entropy corrections. Further, we study the $f(R,~T)$ gravity ($\zeta$), quantum gravity ($\alpha$), and particle kinetic energy ($\Xi$) effect on both temperature and entropy.