The SU(2) Black Hole entropy revisited

TL;DR

This paper revisits SU(2) black hole entropy in loop quantum gravity, incorporating finite-level quantum corrections to improve the accuracy of state-counting for both spherical and distorted black holes.

Contribution

It introduces a method to include quantum group corrections by considering finite Chern-Simons level, refining entropy calculations beyond previous infinite-level assumptions.

Findings

Computed leading entropy terms for SU(2) black holes.

Derived logarithmic corrections considering finite quantum levels.

Extended the framework to distorted black holes.

Abstract

We study the state-counting problem that arises in the SU(2) black hole entropy calculation in loop quantum gravity. More precisely, we compute the leading term and the logarithmic correction of both the spherically symmetric and the distorted SU(2) black holes. Contrary to what has been done in previous works, we have to take into account "quantum corrections" in our framework in the sense that the level k of the Chern-Simons theory which describes the black hole is finite and not sent to infinity. Therefore, the new results presented here allow for the computation of the entropy in models where the quantum group corrections are important.