Quantum geometry and black hole entropy: inclusion of distortion and rotation

TL;DR

This paper extends quantum geometric models of black hole horizons to include distortions and rotations, showing that the entropy formula remains proportional to the horizon area for both spherical and axi-symmetric cases.

Contribution

It generalizes the quantum geometry of black hole horizons from spherical to axi-symmetric geometries, incorporating distortions and rotations.

Findings

Entropy remains proportional to horizon area for type II horizons.

The Barbero-Immirzi parameter value is consistent across types.

The extension includes arbitrary distortions and rotations in quantum horizon models.

Abstract

Equilibrium states of black holes can be modelled by isolated horizons. If the intrinsic geometry is spherical, they are called type I while if it is axi-symmetric, they are called type II. The detailed theory of geometry of quantum type I horizons and the calculation of their entropy can be generalized to type II, thereby including arbitrary distortions and rotations. The leading term in entropy of large horizons is again given by 1/4th of the horizon area for the same value of the Barbero-Immirzi parameter as in the type I case. Ideas and constructions underlying this extension are summarized.