Black Hole Hair Removal: Non-linear Analysis

TL;DR

The paper resolves a discrepancy in microscopic degeneracies between BMPV black holes in flat space and Taub-NUT space by explicitly constructing non-linear hair modes living outside the horizon that preserve supersymmetry. It shows that certain proposed horizon-exterior deformations are singular and thus excluded, while explicit fermionic and bosonic hair modes exist in both 5D and 4D setups, including a 24-boson sector in 4D. Through a careful partition-function analysis that removes hair contributions, the authors demonstrate that the horizon (hair-free) degeneracies match for the two cases. This work solidifies the interpretation that the difference in total degeneracy originates from exterior hair and confirms the common horizon contribution as the universal part of the entropy.

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.