Uniqueness of Five-Dimensional Supersymmetric Black Holes

TL;DR

The work addresses the problem of black hole uniqueness for supersymmetric solutions in five-dimensional ungauged supergravity coupled to multiple abelian vector multiplets. By leveraging a Tod-type classification and a careful near-horizon analysis, the authors show that regular-horizon solutions have near-horizon geometries restricted to $\text{flat}$ space, $AdS_3 \times S^2$, or the BMPV-type geometry, and that globally the only solution with a BMPV near-horizon geometry is the Chamseddine–Sabra BMPV black hole. The result extends the minimal theory uniqueness to non-minimal settings via Very Special geometry, concluding that, under strong regularity assumptions, the Sabra–Chamsedine solution is unique in its class. This solidifies the link between horizon structure and global black hole uniqueness in higher-dimensional supergravity, and outlines open questions about weaker regularity, other horizon branches (e.g., $\Delta=0$), and gauged theories.

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.