Black hole thermodynamics in natural variables: quadrophenia

Abstract

It was recently observed in [1] for thermal Kerr-Newman black holes in 4d flat space that one can rewrite the conventional thermodynamics on the inner and outer horizons in terms of left- and right-moving variables with a remarkable simplification of the corresponding expressions. With the goal of illustrating the wide applicability of these newly proposed natural variables, we extend the original observation in four independent directions that can be further superimposed on each other. These four generalizations can be thought of as different deformations of the original 4d Einstein-Maxwell theory, all within the framework of supergravity: higher derivative (HD) corrections in minimal 4d supergravity; additional scalar and vector couplings in matter-coupled 4d supergravity; higher dimensions, in particular 5d minimal supergravity; and a cosmological constant in 4d minimal gauged supergravity with Anti-de Sitter (AdS) vacuum. Each of these generalizations offers a different lesson about the novel thermodynamics, and we pay special attention to the respective BPS limits that can be understood from fixed point formulae, demonstrating the power of the natural variables to capture the full phase space.

Maximally symmetric nuts in 4d 𝒩 = 2 higher derivative supergravity

“…The simplification of the supergravity action, based on equivariant localization, technically relies only on a U(1) action. This feature is also present in interesting non-BPS backgrounds, such as thermal black holes, which exhibit a rather different form of the supergravity action, see [39,41].. It would be intriguing to formulate an equivariant localization calculation for these backgrounds, potentially unveiling a general principle for evaluating higher derivative (and further quantum and string theoretic) corrections for thermal black holes.…”