Supersymmetric multi-charge AdS_5 black holes

TL;DR

The paper constructs a comprehensive, supersymmetric, asymptotically AdS$_5$ black-hole solution in five-dimensional ${ m N}=1$ gauged supergravity with gauge group ${U(1)}^3$, unifying all previously known AdS$_5$ BPS black holes as special limits. By formulating solutions in a canonical timelike framework with a four-dimensional Kähler base and optimizing the base choice, the authors derive a four-parameter family that reduces to earlier two- and three-parameter cases; the ${U(1)}^3$ specialization yields a concrete four-parameter solution with explicit expressions for the metric, scalars, gauge fields, charges $Q_I$, angular momenta $J_\phi$, $J_\psi$, and mass $M$ constrained by the BPS bound $M = g|J_\phi| + g|J_\psi| + |ar{X}^I Q_I|$. The work confirms AdS$_5$ asymptotics, provides conditions to avoid causal pathologies and a smooth extension through the horizon, and yields a horizon area formula, thereby offering a unified framework to study supersymmetric AdS$_5$ black holes and their potential microscopic entropy interpretations within AdS/CFT. This framework also sets the stage for uplift to type IIB on AdS$_5 imes S^5$ and for exploring entropy calculations via dual gauge theories and index techniques in the large-$N$ limit.

Abstract

A new supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional U(1)^3 gauged supergravity is presented. All known examples of such black holes arise as special cases of this solution, which is characterized by three charges and two angular momenta, with one constraint relating these five quantities. Analagous solutions of U(1)^n gauged supergravity are also presented.