Stability and topological thermodynamics of black holes through modified entropy

Rani S. Riaz H. Zafar U. Jawad A. Myrzakulov N. Shaymatov S.
September 2025 Springer Nature

European Physical Journal C
2025 #85 Issue 9

We explore higher-dimensional black holes (BHs) using the Sharma–Mittal entropy, a widely employed measure in BH thermodynamics due to the non-extensive nature of BHs. We compute different thermodynamic quantities like temperature, heat capacity, and Gibbs free energy to study the stability of higher-dimensional BHs in Einstein–Gauss–Bonnet gravity (EGBG). We explicitly analyze the behavior for different horizon topologies (parameterized by k) in EGBG and observe that these BH exhibit both local and global instability. Additionally, we study the sparsity of Hawking radiation, noting that the sparsity parameter tends to zero as the horizon radius increases. It is also observed that emission of energy radiates most rapidly for larger BHs, which is consistent with physical observations. Furthermore, to support our analysis, we choose thermodynamical topology methods (specifically, the temperature and on-shell Gibbs free energy) to observe the stability of the aforementioned BH solutions. It is found that the total topological charge obtained from the free energy method leads to +1 for specific values of k, which also gives the confirmation of the stability of these BH solutions in EGBG for a specific choice of other constant parameters.

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Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology, Hangzhou, 310023, China
Department of Mathematics, COMSATS University Islamabad, Lahore-Campus, Lahore, 54000, Pakistan
Faculty of Symbiotic Systems Science, Fukushima University, Fukushima, 960-1296, Japan
L. N. Gumilyov Eurasian National University, Astana, 010008, Kazakhstan
Institute of Fundamental and Applied Research, National Research University TIIAME, Kori Niyoziy 39, Tashkent, 100000, Uzbekistan
University of Tashkent for Applied Sciences, Str. Gavhar 1, Tashkent, 100149, Uzbekistan
Western Caspian University, Baku, AZ1001, Azerbaijan
Tashkent State Technical University, Tashkent, 100095, Uzbekistan

Institute for Theoretical Physics and Cosmology
Department of Mathematics
Faculty of Symbiotic Systems Science
L. N. Gumilyov Eurasian National University
Institute of Fundamental and Applied Research
University of Tashkent for Applied Sciences
Western Caspian University
Tashkent State Technical University

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