The New Black Hole Solution with Anisotropic Fluid in f(R,Lm, T) Gravity: Thermodynamics

TL;DR

This paper introduces new analytic black hole solutions in f(R,Lm,T) gravity with anisotropic matter, exploring their thermodynamics and deviations from General Relativity influenced by matter interactions.

Contribution

The work derives novel black hole solutions in f(R,Lm,T) gravity considering anisotropic fluids and analyzes their thermodynamics under various matter fields.

Findings

Deviations from General Relativity depend on matter interactions.

Energy conditions constrain coupling parameters.

Thermodynamic properties vary with matter type and gravity modifications.

Abstract

In this work, we derive a new class of analytic black hole solutions within the framework of f(R,Lm, T) gravity, where the black hole is surrounded by an anisotropic fluid acting as the matter source. We consider both linear and nonlinear forms of the function f(R,Lm, T), enabling a detailed exploration of how anisotropic pressures and different f(R,Lm, T) influence the spacetime structure. Furthermore, we derive the conditions on the coupling parameters (\b{eta}1, \b{eta}2, \b{eta}3) under which the energy conditions are satisfied. Utilising these constraints, we then investigate the thermodynamic behaviour of the resulting black hole solutions in the presence of various matter fields, namely, dust, radiation, and a quintessence field, each characterised by a distinct equation-of-state parameter. An important outcome of this study is that the results obtained deviate from those predicted by standard General Relativity. It is also observed that these deviations depend explicitly on the interaction between the matter Lagrangian Lm and the trace T of the energy-momentum tensor.