Black hole initial data on hyperboloidal slices

TL;DR

This paper extends Bowen-York initial data for black holes to hyperboloidal slices reaching null infinity, solving the initial value problem numerically for various binary black hole configurations with spins and boosts.

Contribution

It introduces a numerical method for constructing black hole initial data on hyperboloidal slices extending to null infinity, including trumpet configurations.

Findings

Successful numerical solutions for unequal mass binary black holes with spins and boosts.

Hyperboloidal slices do not pose additional difficulties at null infinity.

Trumpet configurations are effectively modeled both analytically and numerically.

Abstract

We generalize Bowen-York black hole initial data to hyperboloidal constant mean curvature slices which extend to future null infinity. We solve this initial value problem numerically for several cases, including unequal mass binary black holes with spins and boosts. The singularity at null infinity in the Hamiltonian constraint associated with a constant mean curvature hypersurface does not pose any particular difficulties. The inner boundaries of our slices are minimal surfaces. Trumpet configurations are explored both analytically and numerically.