IIB black hole horizons with five-form flux and KT geometry

TL;DR

This paper classifies near horizon geometries of IIB supergravity black holes with five-form flux, revealing hermitian manifolds with hidden KT geometry and providing explicit examples of such solutions.

Contribution

It identifies three classes of solutions based on Killing spinors, especially highlighting hermitian manifolds with KT geometry and their field equations.

Findings

Solutions include hermitian manifolds with KT geometry.

Field equations relate to torsion H and Hermitian form omega.

Examples include group manifolds and uplifted lower-dimensional black holes.

Abstract

We investigate the near horizon geometry of IIB supergravity black holes with non-vanishing 5-form flux preserving at least two supersymmetries. We demonstrate that there are three classes of solutions distinguished by the choice of Killing spinors. We find that the spatial horizon sections of the class of solutions with an SU(4) invariant pure Killing spinor are hermitian manifolds and admit a hidden Kahler with torsion (KT) geometry compatible with the SU(4) structure. Moreover the Bianchi identity of the 5-form, which also implies the field equations, can be expressed in terms of the torsion H as d(\omega\wedge H)=\partial\bar\partial \omega^2=0, where omega is a Hermitian form. We give several examples of near horizon geometries which include group manifolds, group fibrations over KT manifolds and uplifted geometries of lower dimensional black holes. Furthermore, we show that the class of solutions associated with a Spin(7) invariant spinor is locally a product R^{1,1} x S, where S is a holonomy Spin(7) manifold.