Exact solutions for supersymmetric stationary black hole composites

TL;DR

This paper provides explicit analytic solutions for supersymmetric black hole bound states in four-dimensional N=2 supergravity, expanding understanding of their structure and entropy properties.

Contribution

It introduces a general method to construct explicit solutions based on known entropy formulas, filling a gap in the explicit characterization of black hole composites.

Findings

Explicit solutions can be constructed from entropy formulas.

Examples include simple cases and moduli-dependent entropy.

The approach broadens the understanding of black hole bound states.

Abstract

Four dimensional N=2 supergravity has regular, stationary, asymptotically flat BPS solutions with intrinsic angular momentum, describing bound states of separate extremal black holes with mutually nonlocal charges. Though the existence and some properties of these solutions were established some time ago, fully explicit analytic solutions were lacking thus far. In this note, we fill this gap. We show in general that explicit solutions can be constructed whenever an explicit formula is known in the theory at hand for the Bekenstein-Hawking entropy of a single black hole as a function of its charges, and illustrate this with some simple examples. We also give an example of moduli-dependent black hole entropy.