Numerical Brill-Lindquist initial data with a Schwarzschildean end at spatial infinity

TL;DR

This paper develops a numerical method to create initial data for spacetime simulations that smoothly transition from a Schwarzschild solution at infinity to a Brill-Lindquist configuration in the interior, using Corvino's gluing technique.

Contribution

It introduces a novel gluing approach with angular dependence to connect Schwarzschild and Brill-Lindquist data, analyzing the impact on ADM mass.

Findings

Successful numerical construction of mixed initial data

Demonstration of the gluing method's flexibility

Insights into ADM mass dependence on gluing parameters

Abstract

We construct numerically time-symmetric initial data that are Schwarzschildean at spatial infinity and Brill-Lindquist in the interior. The transition between these two data sets takes place along a finite gluing region equipped with an axisymmetric Brill wave metric. The construction is based on an application of Corvino's gluing method using Brill waves due to Giulini and Holzegel. Here, we use a gluing function that includes a simple angular dependence. We also investigate the dependence of the ADM mass of our construction on the details of the gluing procedure.