Metrics Admitting Killing Spinors In Five Dimensions

TL;DR

The paper addresses constructing general BPS black hole solutions in $d=5$, $N=2$ supergravity with vector multiplets that preserve half of the supersymmetry. It uses Killing spinor equations in a bosonic background with the metric form $ds^2=-e^{-4U}(dt+ w_mdx^m)^2+e^{2U}d\vec{x}^2$ and expresses all fields in terms of harmonic functions via the cubic prepotential ${\cal V}=\frac{1}{6}C_{IJK}X^I X^J X^K$, yielding relations such as $e^{2U}X_I=\frac{1}{3}H_I$ and $F^I_{tm}=-\partial_m(e^{-2U}X^I)$. This framework fixes the solution through harmonic functions and reproduces a broad class of rotating BPS black holes, including explicit results for mass and entropy and connections to known models like STU. The results unify static and rotating cases within very special geometry, providing a geometric basis for microstate and entropy analyses in Calabi-Yau compactifications and laying groundwork for non-extremal extensions. The approach has potential impact on microscopics, holography, and the study of extremal black holes in five dimensions.

Abstract

BPS black hole configurations which break half of supersymmetry in the theory of N=2, d=5 supergravity coupled to an arbitrary number of abelian vector multiplets are discussed. A general class of solutions comprising all known BPS rotating black hole solutions is obtained.