Black Hole Hair Removal: Non-linear Analysis

TL;DR

This paper constructs explicit non-linear hair modes for BMPV black holes in different backgrounds, demonstrating how these modes account for differences in microscopic degeneracies and aligning the partition functions after their removal.

Contribution

It provides the first explicit construction of non-linear hair modes for BMPV black holes, clarifying their role in black hole microstate counting.

Findings

Hair modes are explicitly constructed as finite bosonic and fermionic deformations.

Removing hair contributions aligns the microscopic partition functions of different black holes.

Solutions are shown to be free of curvature singularities at the horizon.

Abstract

BMPV black holes in flat transverse space and in Taub-NUT space have identical near horizon geometries but different microscopic degeneracies. It has been proposed that this difference can be accounted for by different contribution to the degeneracies of these black holes from hair modes, -- degrees of freedom living outside the horizon. In this paper we explicitly construct the hair modes of these two black holes as finite bosonic and fermionic deformations of the black hole solution satisfying the full non-linear equations of motion of supergravity and preserving the supersymmetry of the original solutions. Special care is taken to ensure that these solutions do not have any curvature singularity at the future horizon when viewed as the full ten dimensional geometry. We show that after removing the contribution due to the hair degrees of freedom from the microscopic partition function, the partition functions of the two black holes agree.