Uniqueness of Five-Dimensional Supersymmetric Black Holes

TL;DR

This paper proves a uniqueness theorem for five-dimensional supersymmetric black holes, classifying their possible near-horizon geometries and identifying the specific solutions that exhibit these geometries.

Contribution

It introduces a classification of supersymmetric solutions in five-dimensional supergravity and establishes the uniqueness of the BMPV black hole among solutions with similar near-horizon geometries.

Findings

Near-horizon geometries are flat space, AdS_3 x S^2, or BMPV.

Only the Chamseddine and Sabra solution has BMPV near-horizon geometry.

The classification applies to solutions with regular scalars and gauge fields.

Abstract

A classification of supersymmetric solutions of five dimensional ungauged supergravity coupled to arbitrary many abelian vector multiplets is used to prove a uniqueness theorem for asymptotically flat supersymmetric black holes with regular horizons. It is shown that the near-horizon geometries of solutions for which the scalars and gauge field strengths are sufficiently regular on the horizon are flat space, AdS_3 x S^2, or the near-horizon BMPV solution. Furthermore, the only black hole which has the near-horizon BMPV geometry for its near-horizon geometry is the solution found by Chamseddine and Sabra.