Supersymmetric Black Hole Hair and AdS_3 x S^3

TL;DR

This paper investigates supersymmetric hair modes in AdS_3 x S^3 geometries related to BMPV black holes, revealing their boundary conditions and classification within 6D supergravity solutions.

Contribution

It identifies supersymmetric hair modes in AdS_3 x S^3 and analyzes their boundary conditions, linking them to 6D supergravity solution classifications.

Findings

Supersymmetric hair modes satisfy non-normalisable boundary conditions.

Boundary conditions vary for different hair modes and asymptotic completions.

Hair modes fit into the classification of 6D supergravity solutions.

Abstract

The 4D-5D connection allows us to view the same near horizon geometry as part of a 4D black hole or a 5D black hole. A much studied example of this phenomenon is the BMPV black hole uplifted to 6D with flat base space versus Taub-NUT base space. These black holes have identical near horizon AdS_3 x S^3 geometry. In this paper, we study modes in AdS_3 x S^3 and identify those that correspond to supersymmetric hair modes in the full black hole spacetimes. We show that these modes satisfy non-normalisable boundary conditions in AdS_3. The non-normalisable boundary conditions are different for different hair modes and for different asymptotic completion. We also discuss how the supersymmetric hair modes on BMPV black holes fit into the classification of supersymmetric solutions of 6D supergravity.