https://doi.org/10.1140/epjc/s10052-024-13586-9
Regular Article
Topological classification of critical points for hairy black holes in Lovelock gravity
1
College of Computer and Information Engineering, Guizhou University of Commerce, 550014, Guiyang, China
2
School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing, 100083, Beijing, China
3
School of Physics and Electronic Science, Zunyi Normal University, 563006, Zunyi, China
4
Department of Physics, University of Hradec Králové, Rokitanského 62, 500 03, Hradec Králové, Czechia
5
College of Physics, Guizhou University, 550025, Guiyang, China
Received:
31
August
2024
Accepted:
1
November
2024
Published online:
2
December
2024
In various fields of mathematical research, the Brouwer degree is a potent tool for topological analysis. By using the Brouwer degree defined in one-dimensional space, we interpret the equation of state for temperature in black hole thermodynamics, 
, as a spinodal curve, with its derivative defining a new function f. The sign of the slope of f indicates the topological charge of the black hole’s critical points, and the total topological charge can be deduced from the asymptotic behavior of the function f. We analyze a spherical hairy black hole within the framework of Lovelock gravity, paying particular attention to the topological structure of black hole thermodynamics under Gauss–Bonnet gravity. Here, the sign of the scalar hair parameter influences the topological classification of uncharged black holes. When exploring the thermodynamic topological properties of hairy black holes under cubic Lovelock gravity, we find that the spherical hairy black hole reproduces the thermodynamic topological classification results seen under Gauss–Bonnet gravity.
© The Author(s) 2024
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