Eur. Phys. J. C (2025) 85: 828
https://doi.org/10.1140/epjc/s10052-025-14581-4

Regular Article - Theoretical Physics

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

¹ School of Physics and Electronic Science, Zunyi Normal University, 563006, Zunyi, People’s Republic of China
² School of Physics and Astronomy, China West Normal University, 637002, Nanchong, Sichuan, People’s Republic of China
³ College of Computer and Information Engineering, Guizhou University of Commerce, 550014, Guiyang, China
⁴ Departamento de Física Teórica, Atómica y Optica and Laboratory for Disruptive Interdisciplinary Science (LaDIS), Universidad de Valladolid, 47011, Valladolid, Spain
⁵ Department of Physics, University of Hradec Králové, Rokitanského 62, 500 03, Hradec Králové, Czechia
⁶ College of Physics, Guizhou University, 550025, Guiyang, Guizhou, People’s Republic of China

^a haochen1249@yeah.net

Received: 4 June 2025
Accepted: 23 July 2025
Published online: 1 August 2025

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.