Numerical Approach for Corvino-Type Gluing of Brill-Lindquist Initial Data

TL;DR

This paper introduces a new numerical method to glue Schwarzschild and Brill-Lindquist initial data for Einstein's equations, improving accuracy and flexibility in constructing initial conditions for numerical relativity.

Contribution

It develops a novel numerical approach that decomposes an overdetermined Poisson problem, enabling highly accurate gluing of different initial data sets in general relativity.

Findings

The method achieves high convergence accuracy.

Various ADM masses can be glued at the same radius.

The approach extends previous strategies with improved solvability.

Abstract

Building on the work of Giulini and Holzegel (2005), a new numerical approach is developed for computing Cauchy data for Einstein's equations by gluing a Schwarzschild end to a Brill-Lindquist metric via a Corvino-type construction. In contrast to, and in extension of, the numerical strategy of Doulis and Rinne (2016), the overdetermined Poisson problem resulting from the Brill wave ansatz is decomposed to obtain two uniquely solvable problems. A pseudospectral method and Newton-Krylov root finder are utilized to perform the gluing. The convergence analysis strongly indicates that the numerical strategy developed here is able to produce highly accurate results. It is observed that Schwarzschild ends of various ADM masses can be glued to the same interior configuration using the same gluing radius.