General BPS Black Holes In Five Dimensions

TL;DR

This paper constructs the most general static BPS black hole solutions in five-dimensional $N=2$ supergravity coupled to an arbitrary number of Abelian vector multiplets, with dynamics governed by very special geometry through a cubic prepotential ${ m V}=rac{1}{6}C_{IJK}X^I X^J X^K$. By solving the gravitino and gaugino SUSY variations, it shows the solutions preserve half the supersymmetry and that the moduli flow to horizon values that extremize the central charge $Z$, leading to attractor behavior. The work provides explicit expressions for the metric, gauge fields, and moduli in terms of harmonic functions $H_I$, and illustrates the STU model in detail, highlighting implications for M-theory on Calabi–Yau threefolds and phase transitions such as flop transitions. These results connect BPS black holes to the moduli-space structure of Calabi-Yau compactifications, offering tools to probe non-perturbative transitions in five dimensions.

Abstract

We construct general static black hole configuration for the theory of N=2, d=5 supergravity coupled to an arbitrary number of Abelian vector multiplets. The underlying very special geometry structure plays a major role in this construction. From the viewpoint of M-theory compactified on a Calabi-Yau threefold, these black holes are identified with BPS winding states of the membrane around 2-cycles of the Calabi-Yau threefold, and thus are of importance in the probing of the phase transitions in the moduli space of M-theory compactified on a Calabi-Yau threefold.