Isolated horizons in numerical relativity: constructing the excised Kerr spacetime in Dirac gauge

TL;DR

This paper develops a method to construct initial data for black hole spacetimes in general relativity using isolated horizon formalism and Dirac gauge, providing insights into the conformal metric and the conformally flat approximation.

Contribution

It introduces a constrained formalism in Dirac gauge for excised black hole initial data, especially addressing the conformal metric and horizon boundary conditions.

Findings

A no-boundary treatment on the horizon is feasible for the conformal metric equation.

The method assesses the validity of the conformally flat approximation in black hole initial data.

Results relate to and improve upon previous approaches in numerical relativity.

Abstract

Using a constrained formalism for Einstein equations in Dirac gauge, we propose to compute excised quasistationary initial data for black hole spacetimes in full general relativity. Vacuum spacetime settings are numerically constructed by using the isolated horizon formalism; we especially tackle the conformal metric part of our equations, assuming global stationarity. We show that a no-boundary treatment can be used on the horizon for the equation related to the conformal metric. We relate this finding to previous suggestions in the literature, and use our results to assess the widely used conformally flat approximation for computing black hole initial data.