Phase-space and Black Hole Entropy of Higher Genus Horizons in Loop Quantum Gravity

TL;DR

This paper extends loop quantum gravity to higher genus horizons, deriving a phase-space framework that accounts for genus cycles, and confirms the Bekenstein-Hawking entropy law with genus-dependent modifications.

Contribution

It constructs the phase-space for higher genus isolated horizons in loop quantum gravity and calculates the entropy, revealing genus cycle effects on sub-leading terms.

Findings

Leading entropy term matches A/4 law

Genus cycles modify sub-leading entropy contributions

Phase-space dimension includes genus cycle degrees of freedom

Abstract

In the context of loop quantum gravity, we construct the phase-space of isolated horizons with genus greater than 0. Within the loop quantum gravity framework, these horizons are described by genus g surfaces with N punctures and the dimension of the corresponding phase-space is calculated including the genus cycles as degrees of freedom. From this, the black hole entropy can be calculated by counting the microstates which correspond to a black hole of fixed area. We find that the leading term agrees with the A/4 law and that the sub-leading contribution is modified by the genus cycles.