Isolated Horizon structures in quasiequilibrium black hole initial data

TL;DR

This paper proposes using the full isolated horizon structure in solving Einstein equations for quasiequilibrium black hole initial data, extending previous approaches that only used nonexpanding horizons, to better determine the shape of the excision surface.

Contribution

It introduces a novel method incorporating the complete isolated horizon structure into elliptic systems for black hole initial data, improving boundary condition determination.

Findings

Enhanced boundary conditions for black hole excision surfaces.

More accurate modeling of black hole horizons in initial data.

Extension of previous nonexpanding horizon methods.

Abstract

Isolated horizon conditions enforce the time invariance of both the intrinsic and the extrinsic geometry of a (quasilocal) black hole horizon. Nonexpanding horizons, only requiring the invariance of the intrinsic geometry, have been successfully employed in the (excision) initial data of black holes in instantaneous equilibrium. Here we propose the use of the full isolated horizon structure when solving the elliptic system resulting from the complete set of conformal 3+1 Einstein equations under a quasiequilibrium ansatz prescription. We argue that a set of geometric inner boundary conditions for this extended elliptic system then follows, determining the shape of the excision surface.