Toric Kahler metrics and AdS_5 in ring-like co-ordinates

TL;DR

This paper explores a class of toric Kahler metrics that unify the description of asymptotically flat and AdS supersymmetric solutions in five-dimensional supergravity, introducing ring-like coordinates and proposing an Ansatz for AdS black rings.

Contribution

It introduces a unified framework using toric Kahler metrics with ring-like coordinates to describe supersymmetric solutions in five dimensions, including potential black rings in AdS.

Findings

Toric Kahler metrics can describe both flat and AdS solutions.

Darboux coordinates are ring-like in this framework.

An Ansatz for supersymmetric black rings in AdS is proposed.

Abstract

Stationary, supersymmetric supergravity solutions in five dimensions have Kahler metrics on the four-manifold orthogonal to the orbits of a time-like Killing vector. We show that an explicit class of toric Kahler metrics provide a unified framework in which to describe both the asymptotically flat and asymptotically AdS solutions. The Darboux co-ordinates used for the local description turn out to be ''ring-like.'' We conclude with an Ansatz for studying the existence of supersymmetric black rings in AdS.