A topological charge of black holes

Abstract

The topological charge of a maximally symmetric black hole naturally arises in holography, which can be viewed as the last charge of the black hole in the sense that it together with all other known charges satisfies the holographic Gibbs-Duhem-like relation as a completeness relation. It is then observed that this topological charge, which we have missed before, fits perfectly into the black hole thermodynamics from two different approaches, not only in Einstein's gravity, but also in the general Lovelock-Maxwell theory.

8 pages, 1 table; v2: title changed from "The last (lost) charge of a black hole" to "A topological charge of black holes", version published in CQG

References in corpus (7)

• Nonlinear Fluid Dynamics from Gravity
• Smarr Formula and an Extended First Law for Lovelock Gravity
• Holographic Entropy Production
• A Hamiltonian approach for the Thermodynamics of AdS black holes
• First law of thermodynamics on holographic screens in entropic force frame
• Dynamics of Gravity as Thermodynamics on the Spherical Holographic Screen
• Phase Transition of RN-AdS Black Hole with Fixed Electric Charge and Topological Charge

Cited by in corpus (6)

• Restricted phase space thermodynamics for AdS black holes via holography
• Thermodynamics for higher dimensional rotating black holes with variable Newton constant
• Restricted phase space thermodynamics for black holes in higher dimensions and higher curvature gravities
• The topological RN-AdS black holes cannot be overcharged by the new version of gedanken experiment
• Topological black holes in Einstein-Maxwell and 4D conformal gravities revisited
• Asymptotic critical behavior of holographic phase transition at finite topological charge -- the spectrum of excited states becomes continuous at $T=0$