Introduction to Isolated Horizons in Numerical Relativity

TL;DR

This paper introduces a coordinate-independent method based on isolated horizons for accurately extracting mass and angular momentum of black holes in numerical simulations, applicable at various stages of black hole evolution.

Contribution

It presents a novel, intrinsic, coordinate-independent approach for measuring black hole properties in numerical relativity using the isolated horizon framework.

Findings

Method works at early and late times in simulations.

Allows calculation of J and M from intrinsic horizon quantities.

Provides a numerical technique for finding the rotational symmetry vector.

Abstract

We present a coordinate-independent method for extracting mass (M) and angular momentum (J) of a black hole in numerical simulations. This method, based on the isolated horizon framework, is applicable both at late times when the black hole has reached equilibrium, and at early times when the black holes are widely separated. We show how J and M can be determined in numerical simulations in terms of only those quantities which are intrinsic to the apparent horizon. We also present a numerical method for finding the rotational symmetry vector field (required to calculate J) on the horizon.