Excision boundary conditions for black hole initial data

TL;DR

This paper introduces and tests a set of boundary conditions for black hole excision surfaces in initial data, enabling quasiequilibrium configurations with arbitrary spins, applicable to single and binary black hole systems.

Contribution

It presents a general, extensively tested set of boundary conditions for black hole initial data that can be used with any conformal geometry and slicing, including spin specification.

Findings

Boundary conditions successfully produce quasiequilibrium black hole data.

They work well for both single and binary black hole systems.

The lapse boundary condition appears to be part of the initial gauge choice.

Abstract

We define and extensively test a set of boundary conditions that can be applied at black hole excision surfaces when the Hamiltonian and momentum constraints of general relativity are solved within the conformal thin-sandwich formalism. These boundary conditions have been designed to result in black holes that are in quasiequilibrium and are completely general in the sense that they can be applied with any conformal three-geometry and slicing condition. Furthermore, we show that they retain precisely the freedom to specify an arbitrary spin on each black hole. Interestingly, we have been unable to find a boundary condition on the lapse that can be derived from a quasiequilibrium condition. Rather, we find evidence that the lapse boundary condition is part of the initial temporal gauge choice. To test these boundary conditions, we have extensively explored the case of a single black hole and the case of a binary system of equal-mass black holes, including the computation of quasi-circular orbits and the determination of the inner-most stable circular orbit. Our tests show that the boundary conditions work well.