Thermodynamic stability of the new black hole solution in $f(R,G,T)$ gravity

Abstract

In this literature, we derive an approximate black hole metric within the \( f(R, G, T) \) gravity framework, where the black hole is surrounded by an anisotropic fluid as the matter source. This approach allows us to study the influence of anisotropic pressures on the black hole structure. We then investigate the thermodynamic properties of the approximate solution, considering various types of matter fields. We analyze the thermodynamic quantities such as Wald's entropy, Hawking temperature, and specific heat for each case. After examining the specific heat, we find that the black holes are thermodynamically stable, with positive specific heat values indicating stability. This result suggests that the black holes under these conditions do not undergo thermal instability, ensuring their long-term viability.