Stationary solutions of N=2 supergravity

TL;DR

This paper analyzes stationary solutions in N=2 supergravity, showing they are determined by harmonic functions and exploring various black hole and instanton solutions within this framework.

Contribution

It provides a general method to derive stationary solutions in N=2 supergravity, including new insights into black holes and instantons with specific geometric conditions.

Findings

Solutions are characterized by harmonic functions.

Includes rotating black holes, Taub-NUT, and Eguchi-Hanson instantons.

Discusses worldsheet instanton corrections near Calabi-Yau cycles.

Abstract

We discuss general bosonic stationary configurations of N=2, D=4 supergravity coupled to vector multiplets. The requirement of unbroken supersymmetries imposes constraints on the holomorphic symplectic section of the underlying special K\"ahler manifold. The corresponding solutions of the field equations are completely determined by a set of harmonic functions. As examples we discuss rotating black holes, Taub-NUT and Eguchi-Hanson like instantons for the STU model. In addition, we discuss, in the static limit, worldsheet instanton corrections to the STU black hole solution, in the neighbourhood of a vanishing 4-cycle of the Calabi-Yau manifold. Our procedure is quite general and includes all known black hole solutions that can be embedded into N=2 supergravity.