Black Hole Hair Removal

TL;DR

This paper investigates black hole microstate degeneracies and proposes that external degrees of freedom, or 'hair', account for discrepancies in microscopic spectra between related black holes, aligning their entropy calculations.

Contribution

It introduces the concept of black hole hair to explain differences in microstate degeneracies for black holes with identical near horizon geometries.

Findings

Identifies black hole hair as external degrees of freedom affecting microstate counts.

Shows removal of hair contributions aligns microstate degeneracies for 4D and 5D black holes.

Supports the idea that black hole entropy can be fully accounted for by near horizon data plus hair.

Abstract

Macroscopic entropy of an extremal black hole is expected to be determined completely by its near horizon geometry. Thus two black holes with identical near horizon geometries should have identical macroscopic entropy, and the expected equality between macroscopic and microscopic entropies will then imply that they have identical degeneracies of microstates. An apparent counterexample is provided by the 4D-5D lift relating BMPV black hole to a four dimensional black hole. The two black holes have identical near horizon geometries but different microscopic spectrum. We suggest that this discrepancy can be accounted for by black hole hair, -- degrees of freedom living outside the horizon and contributing to the degeneracies. We identify these degrees of freedom for both the four and the five dimensional black holes and show that after their contributions are removed from the microscopic degeneracies of the respective systems, the result for the four and five dimensional black holes match exactly.