Revisiting thermodynamic topologies of black holes

Abstract

In the generalized off-shell free energy landscape, black holes can be treated as thermodynamic topological defects. The local topological properties of the spacetime can be reflected by the winding numbers at the defects, while the global topological nature can be classified by the topological number which is the sum of all local winding numbers. We propose that the winding numbers can be calculated via the residues of isolated one-order pole points of characterized functions constructed from the off-shell free energy. Using the residue method, we show that the topologies of black holes can be divided into three classes with the topological numbers being -1, 0, and 1, respectively, being consistent with the results obtained in [Phys. Rev. Lett. 129, 191101 (2022)] by using the topological current method. Moreover, we point out that standard defect points, generation and annihilation points, and critical points can be distinguished by coefficients of the Laurent series of the off-shell characterized function at those singular points.

18 pages

References in corpus (10)

• Light ring stability in ultra-compact objects
• Black Hole Solutions as Topological Thermodynamic Defects
• Topology of black hole thermodynamics
• Topology of black hole thermodynamics in Gauss-Bonnet gravity
• Topology of critical points and Hawking-Page transition
• Topology of Born-Infeld AdS black holes in 4D novel Einstein-Gauss-Bonnet gravity
• Multi-critical Points in Black Hole Phase Transitions
• Generalized free energy landscape of black hole phase transition
• Black Holes With Many Horizons in the Theories of Nonlinear Electrodynamics
• Path integral and instantons for the process and phase transition rate of the RNAdS black hole

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