Generic isolated horizons in loop quantum gravity

TL;DR

This paper extends the loop quantum gravity quantization of isolated horizons from symmetric cases to arbitrary shapes, showing that the quantum geometry and entropy results remain consistent.

Contribution

It introduces a quantum theory for generic-shaped horizons in loop quantum gravity, generalizing previous symmetric models.

Findings

Hilbert space for all generic horizons matches symmetric case

Horizon entropy remains proportional to area

Barbero-Immirzi parameter value is unchanged

Abstract

Isolated horizons model equilibrium states of classical black holes. A detailed quantization, starting from a classical phase space restricted to spherically symmetric horizons, exists in the literature and has since been extended to axisymmetry. This paper extends the quantum theory to horizons of arbitrary shape. Surprisingly, the Hilbert space obtained by quantizing the full phase space of \textit{all} generic horizons with a fixed area is identical to that originally found in spherical symmetry. The entropy of a large horizon remains one quarter its area, with the Barbero-Immirzi parameter retaining its value from symmetric analyses. These results suggest a reinterpretation of the intrinsic quantum geometry of the horizon surface.