Universal thermodynamic topological classes of static black holes in Conformal Killing Gravity

TL;DR

This paper classifies static black holes in Conformal Killing Gravity into universal thermodynamic topological classes, revealing how this gravity theory significantly alters black hole thermodynamics and stability across different regimes.

Contribution

It introduces a universal topological classification scheme for black holes in Conformal Killing Gravity, expanding understanding of their thermodynamic properties and stability.

Findings

Black holes are classified into specific topological categories based on CKG parameters.

Thermodynamic properties of black holes are significantly reconstructed in CKG.

Stability of black holes varies with temperature regimes and CKG parameters.

Abstract

In this study, we develop universal thermodynamic topological classes for the static black holes in the context of the Conformal Killing Gravity. Our findings indicate that the Conformal Killing Gravity significantly reconstructs the thermodynamic properties of both the smallest inner and the largest outer black hole states. Additionally, it considerably alters the thermodynamic stability of black holes across both high-temperature and low-temperature regimes. This analysis shows that different CKG parameter settings will lead to $W^{0+}$ $(\lambda>0)$ and $W^{1+}$ $(\lambda<0)$ categories for the charged AdS black hole, the Reissner-Nordstr$\ddot{o}$m black hole in Conformal Killing Gravity is classified into the $W^{0+}$ and $W^{1+}$ categories. Furthermore, we examine the specific scenario where charge is neglected. The study reveals that within the framework of Conformal Killing Gravity, the Schwarzschild black hole similar to the Schwarzschild-AdS black hole, can be classified into the $W^{1-}$ and $W^{0-}$ categories. This work provides key insights into the fundamental nature of quantum gravity theory.