Black Hole Solutions as Topological Thermodynamic Defects

Abstract

In this work, employing the generalized off-shell free energy, we treat black hole solutions as defects in the thermodynamic parameter space. The results show that the positive and negative winding numbers corresponding to the defects indicate the local thermodynamical stable and unstable black hole solutions, respectively. The topological number $W$ defined as the sum of the winding numbers for all the black hole branches at an arbitrary given temperature is found to be a universal number independent of the black hole parameters. Moreover, this topological number only depends on the thermodynamic asymptotic behaviors of the black hole temperature at small and large black hole limits. Different black hole systems are characterized by three classes via this topological number. This number could help us well understanding the black hole thermodynamics, and further shed new light on the fundamental nature of quantum gravity.

arXiv comment7 pages, 4 figures, supplemental material is added. Version published in Physical Review Letters, selected as Editors' Suggestion

References in corpus (21)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• P-V criticality of charged AdS black holes
• Charged AdS Black Holes and Catastrophic Holography
• Enthalpy and the Mechanics of AdS Black Holes
• Kerr black holes with scalar hair
• Dilatonic Black Holes in Higher Curvature String Gravity
• Spontaneous scalarization of black holes and compact stars from a Gauss-Bonnet coupling
• Light ring stability in ultra-compact objects
• Spontaneous scalarisation of charged black holes
• Spontaneously scalarised Kerr black holes
• Stationary black holes and light rings
• Spin-induced black hole scalarization in Einstein-scalar-Gauss-Bonnet theory
• Topology of black hole thermodynamics
• Topological Charge and Black Hole Photon Spheres
• Analytical representation for metrics of scalarized Einstein-Maxwell black holes and their shadows
• Universal Properties of Light Rings for Stationary Axisymmetric Spacetimes
• Thermal Dynamic Phase Transition of Reissner-Nordström Anti-de Sitter Black Holes on Free Energy Landscape
• Evolution of the Chern-Simons Vortices
• Critical phenomena in dynamical scalarization of charged black hole
• Dynamic properties of thermodynamic phase transition for five-dimensional neutral Gauss-Bonnet AdS black hole on free energy landscape

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