Constructing near-horizon geometries in supergravities with hidden symmetry

TL;DR

This paper classifies near-horizon geometries in supergravity theories with symmetries, providing a method to determine their form and constructing explicit solutions, including a five-parameter example relevant to extremal black rings.

Contribution

It introduces a general approach to classify near-horizon geometries in supergravity theories with symmetries, and constructs explicit solutions including a novel five-parameter geometry.

Findings

Classification method for near-horizon geometries in supergravity

Explicit construction of a five-parameter near-horizon solution

Insights into extremal black ring geometries

Abstract

We consider the classification of near-horizon geometries in a general two-derivative theory of gravity coupled to abelian gauge fields and uncharged scalars in four and five dimensions, with one and two commuting rotational symmetries respectively. Assuming that the theory of gravity reduces to a 3d non-linear sigma model (as is typically the case for ungauged supergravities), we show that the functional form of any such near-horizon geometry may be determined. As an example we apply this to five dimensional minimal supergravity. We also construct an example of a five parameter near-horizon geometry solution to this theory with S^1 X S^2 horizon topology. We discuss its relation to the near-horizon geometries of the yet to be constructed extremal black rings with both electric and dipole charges.