The dark (BPS) side of thermodynamics in Minkowski${}_4$

Abstract

We explore the BPS limit of asymptotically flat black hole thermodynamics, drawing analogies with recent studies of black holes in anti-de Sitter space. Although ultimately motivated by supersymmetry and quantum gravity, the BPS limit is classically well-defined for the dyonic Kerr-Newman black holes in pure Einstein-Maxwell theory and various generalizations with additional scalars and gauge fields that admit embedding in $\mathcal{N}=2$ supergravity (for concreteness we consider the STU model). This limit is manifestly different from extremality as it includes a family of rotating Euclidean saddles that represent a (fictitious) thermal branch, smoothly connected with the extremal static Reissner-Nordström black hole and its generalizations with extra matter. We are able to evaluate unambiguously all BPS chemical potentials, finding constant imaginary angular velocity as a consequence of Wick rotation. In the mixed ensemble of fixed magnetic and varying electric charges, we derive the OSV formula that is crucial for the microscopic understanding of the system, and provide evidence that it should be interpreted as a fixed-point formula.

arXiv comment20 pages, 1 figure, 1 Mathematica file included; v2 minor corrections

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• Explicit black hole thermodynamics in natural variables
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• Black hole thermodynamics at 4 derivatives, natural variables and BPS limits
• Index saddle for supersymmetric F1-P black ring