Quasi--local angular momentum of non--symmetric isolated and dynamical horizons from the conformal decomposition of the metric

TL;DR

This paper introduces a new, general definition of quasi-local angular momentum for non-axisymmetric horizons using conformal decomposition, extending the standard approach to more complex geometries.

Contribution

It proposes a novel, fully general method for defining quasi-local angular momentum based on conformal symmetry, applicable to non-symmetric horizons.

Findings

The new definition agrees with the standard in axisymmetric cases.

It extends angular momentum concepts to non-symmetric marginally outer trapped surfaces.

The approach is based on conformal decomposition of the metric.

Abstract

A new definition of quasi--local angular momentum of non--axisymmetric marginally outer trapped surfaces is proposed. It is based on conformal decomposition of the two--dimensional metric and the action of the group of conformal symmetries. The definition is completely general and agrees with the standard one in axi--symmetric surfaces.