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

TL;DR

This paper investigates the BPS limit of asymptotically flat black hole thermodynamics, revealing new insights into chemical potentials, Euclidean saddles, and the OSV formula within Einstein-Maxwell and supergravity frameworks.

Contribution

It introduces a well-defined BPS limit for flat black holes, including rotating Euclidean saddles, and derives the OSV formula in a mixed charge ensemble, connecting thermodynamics with microscopic interpretations.

Findings

Unambiguous evaluation of BPS chemical potentials.

Identification of a family of rotating Euclidean saddles.

Derivation of the OSV formula as a fixed-point expression.

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-Nordstr\"om 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.