On a class of 4D Kahler bases and AdS_5 supersymmetric Black Holes

TL;DR

This paper constructs a class of four-dimensional toric Kähler manifolds serving as bases for known and new supersymmetric AdS_5 black hole solutions, revealing a differential equation governing these geometries and exploring their deformations.

Contribution

It introduces a new class of toric Kähler bases for AdS_5 black holes and derives a sixth order differential equation governing their metrics.

Findings

Includes all known asymptotically AdS_5 black holes

Identifies a sixth order differential equation for the metric function H(x)

Discovers infinite supersymmetric deformations with fewer symmetries

Abstract

We construct a class of toric Kahler manifolds, M_4, of real dimension four, a subset of which corresponds to the Kahler bases of all known 5D asymptotically AdS_5 supersymmetric black-holes. In a certain limit, these Kahler spaces take the form of cones over Sasaki spaces, which, in turn, are fibrations over toric manifolds of real dimension two. The metric on M_4 is completely determined by a single function H(x), which is the conformal factor of the two dimensional space. We study the solutions of minimal five dimensional gauged supergravity having this class of Kahler spaces as base and show that in order to generate a five dimensional solution H(x) must obey a simple sixth order differential equation. We discuss the solutions in detail, which include all known asymptotically AdS_5 black holes as well as other spacetimes with non-compact horizons. Moreover we find an infinite number of supersymmetric deformations of these spacetimes with less spatial isometries than the base space. These deformations vanish at the horizon, but become relevant asymptotically.