Numerical construction of initial data for Einstein's equations with static extension to space-like infinity

TL;DR

This paper introduces a numerical method using pseudo-spectral techniques to construct initial data for Einstein's equations that extend to space-like infinity by gluing Schwarzschild and Brill-Lindquist data, with convergence validation and mass analysis.

Contribution

It presents a novel numerical approach for constructing initial data with space-like infinity extension using Corvino's gluing method in vacuum axisymmetric spacetimes.

Findings

Successful implementation of pseudo-spectral methods for gluing initial data.

Extensive convergence tests validate the numerical results.

Analysis of how the gluing affects the ADM mass.

Abstract

We describe a numerical method to construct Cauchy data extending to space-like infinity based on Corvino's (2000) gluing method. Adopting the setting of Giulini and Holzegel (2005), we restrict ourselves here to vacuum axisymmetric spacetimes and glue a Schwarzschildean end to Brill-Lindquist data describing two non-rotating black holes. Our numerical implementation is based on pseudo-spectral methods, and we carry out extensive convergence tests to check the validity of our numerical results. We also investigate the dependence of the total ADM mass on the details of the gluing construction.