Superradiance and statistical entropy of hairy black hole in three dimensions

TL;DR

This paper computes the statistical entropy of a rotating hairy black hole in three dimensions, incorporating superradiant modes, and finds that the entropy obeys the area law with UV cutoff independent of the gravitational hair.

Contribution

It introduces a method to calculate black hole entropy considering superradiant modes and shows the UV cutoff is unaffected by gravitational hair.

Findings

Entropy follows the area law independent of gravitational hair.

Matter field energy depends on black hole mass, angular momentum, and gravitational hair.

Matter field angular momentum is proportional to black hole angular momentum.

Abstract

We calculate the statistical entropy of a rotating hairy black hole by taking into account superradiant modes in the brick wall method. The UV cutoff is independent of the gravitational hair, which gives the well-defined area law of the entropy. It can be shown that the angular momentum and the energy of matter field depend on the gravitational hair. For the vanishing gravitational hair, it turns out that the energy for matter is related to both the black hole mass and the black hole angular momentum whereas the angular momentum for matter field is directly proportional to the angular momentum of the black hole.