A simple method of constructing binary black hole initial data

TL;DR

This paper introduces a straightforward method for constructing initial data for binary black hole simulations by superposing Kerr-Schild black holes using a parabolic-hyperbolic formulation, linking post-Newtonian and relativistic approaches.

Contribution

The method simplifies initial data construction for binary black holes without boundary conditions in the strong field, connecting PN parameters with relativistic initial data.

Findings

The method effectively reproduces physical parameters of binary black holes.

It provides a direct way to compute ADM charges from input parameters.

The approach facilitates initial data setup for numerical relativity simulations.

Abstract

By applying a parabolic-hyperbolic formulation of the constraints and superposing Kerr-Schild black holes, a simple method is introduced to initialize time evolution of binary systems. As the input parameters are essentially the same as those used in the post-Newtonian (PN) setup the proposed method interrelates various physical expressions applied in PN and in fully relativistic formulations. The global ADM charges are also determined by the input parameters, and no use of boundary conditions in the strong field regime is made.