Flux-area operator and black hole entropy

TL;DR

This paper introduces a new flux-area operator with equidistant eigenvalues for space-times with inner boundaries, simplifying black hole entropy calculations in loop quantum gravity and aligning with the Bekenstein-Hawking law.

Contribution

It proposes a novel flux-area operator with equidistant eigenvalues and demonstrates its advantages in defining and calculating black hole entropy.

Findings

New flux-area operator with equidistant eigenvalues

Simplified black hole entropy calculation method

Asymptotic behavior consistent with Bekenstein-Hawking law

Abstract

We show that, for space-times with inner boundaries, there exists a natural area operator different from the standard one used in loop quantum gravity. This new flux-area operator has equidistant eigenvalues. We discuss the consequences of substituting the standard area operator in the Ashtekar-Baez-Corichi-Krasnov definition of black hole entropy by the new one. Our choice simplifies the definition of the entropy and allows us to consider only those areas that coincide with the one defined by the value of the level of the Chern-Simons theory describing the horizon degrees of freedom. We give a prescription to count the number of relevant horizon states by using spin components and obtain exact expressions for the black hole entropy. Finally we derive its asymptotic behavior, discuss several issues related to the compatibility of our results with the Bekenstein-Hawking area law and the relation with Schwarzschild quasi-normal modes.