Notes on Isolated Horizons

TL;DR

This paper provides a comprehensive framework for analyzing and classifying isolated horizons using null tetrads and spin coefficients, introducing symmetry classes, coordinate systems, and angular momentum definitions.

Contribution

It introduces a general analysis method for isolated horizons, identifies freely specifiable spin coefficients, and classifies symmetry classes with coordinate and angular momentum definitions.

Findings

Classification of isolated horizons into symmetry classes

Introduction of spherical coordinates for horizons with spatial isometries

Definition of angular momentum for isolated horizons

Abstract

A general analysis for characterizing and classifying `isolated horizons' is presented in terms of null tetrads and spin coefficients. The freely specifiable spin coefficients corresponding to isolated horizons are identified and specific symmetry classes are enumerated. For isolated horizons admitting at least one spatial isometry, a standard set of spherical coordinates are introduced and associated metric is obtained. An angular momentum is also defined.