Approximation of the naive black hole degeneracy

TL;DR

This paper explores the calculation of quantum corrections to black hole entropy by analyzing the naive degeneracy spectrum and deriving relations between the area spectrum and degeneracy, focusing on the initial step before applying constraints.

Contribution

It provides a method to approximate the naive black hole degeneracy and solves the infinite relations between the area spectrum and degeneracy.

Findings

Derived the full solution to the infinite relations

Established a procedure for calculating quantum corrections

Focused on the initial step before applying constraints

Abstract

In 1996, Rovelli suggested a connection between black hole entropy and the area spectrum. Using this formalism and a theorem we prove in this paper, we briefly show the procedure to calculate the quantum corrections to the Bekenstein-Hawking entropy. One can do this by two steps. First, one can calculate the "naive" black hole degeneracy without the projection constraint (in case of the U(1) symmetry reduced framework) or the SU(2) invariant subspace constraint (in case of the fully SU(2) framework). Second, then one can impose the projection constraint or the SU(2) invariant subspace constraint, obtaining logarithmic corrections to the Bekenstein-Hawking entropy. In this paper, we focus on the first step and show that we obtain infinite relations between the area spectrum and the naive black hole degeneracy. Promoting the naive black hole degeneracy into its approximation, we obtain the full solution to the infinite relations.