entanglement entropy

event horizon

hawking radiation

regular black

ads black

hawking temperature

black hole thermodynamics

hole solutions

black hole solutions

Physical Review Letters

In this Letter, 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 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 in better understanding the black hole thermodynamics and, further, shed new light on the fundamental nature of quantum gravity.Received 12 August 2022Accepted 10 October 2022DOI:https://doi.org/10.1103/PhysRevLett.129.191101© 2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasGeneral relativityGeneral relativity formalismThermodynamicsPhysical SystemsClassical black holesGravitation, Cosmology & Astrophysics

Black Hole Solutions as Topological Thermodynamic Defects