Uniqueness of supersymmetric AdS$_5$ black holes with $SU(2)$ symmetry

TL;DR

This paper proves the uniqueness of supersymmetric AdS$_5$ black holes with $SU(2)$ symmetry, showing they are either Gutowski-Reall black holes or their near-horizon geometries, and explores related soliton solutions with enhanced symmetry.

Contribution

It establishes a uniqueness theorem for supersymmetric AdS$_5$ black holes with $SU(2)$ symmetry and characterizes soliton solutions with enhanced symmetry in five-dimensional supergravity.

Findings

Any such black hole is a Gutowski-Reall solution or its near-horizon geometry.

Soliton solutions with $SU(2)$ symmetry and nuts or bolts have $U(1) imes SU(2)$ symmetry.

Constructed a family of asymptotically AdS$_5/ ext{Z}_p$ solitons with bolts for $p \,\geq\, 3$.

Abstract

We prove that any supersymmetric solution to five-dimensional minimal gauged supergravity with $SU(2)$ symmetry, that is timelike outside an analytic horizon, is a Gutowski-Reall black hole or its near-horizon geometry. The proof combines a delicate near-horizon analysis with the general form for a K\"ahler metric with cohomogeneity-1 $SU(2)$ symmetry. We also prove that any timelike supersymmetric soliton solution to this theory, with $SU(2)$ symmetry and a nut or a complex bolt, has a K\"ahler base with enhanced $U(1)\times SU(2)$ symmetry, and we exhibit a family of asymptotically AdS$_5/\mathbb{Z}_p$ solitons for $p \geq 3$ with a bolt in this class.