Revisiting thermodynamic topologies of black holes

A bstract 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 topolo...

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Published in:The journal of high energy physics Vol. 2023; no. 1; pp. 102 - 17
Main Authors: Fang, Chaoxi, Jiang, Jie, Zhang, Ming
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 19.01.2023
Springer Nature B.V
SpringerOpen
Subjects:
Approximation
Black Holes
Classical and Quantum Gravitation
Classical Theories of Gravity
Critical point
Defects
Elementary Particles
Energy
Free energy
High energy physics
Mathematical analysis
Phase transitions
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Residues
Spacetime
String Theory
Thermodynamics
Topology
Winding
Classical Theories of Gravity
Black Holes
ISSN:1029-8479, 1029-8479
Online Access:Get full text
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Summary:A bstract 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.
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP01(2023)102