Numerical space-times near space-like and null infinity. The spin-2 system on Minkowski space

TL;DR

This paper demonstrates the first successful numerical solution of the linearized conformal field equations near spacelike infinity on Minkowski space, advancing the use of conformal methods in numerical relativity.

Contribution

It introduces a numerical approach to solve the spin-2 system near spacelike infinity, validating the method with convergence tests and comparisons to exact solutions.

Findings

Numerical solutions match exact solutions for various initial data.

Violations of smoothness conditions lead to predicted singularities.

The method is a promising step for conformal approaches in numerical relativity.

Abstract

In this paper we demonstrate for the first time that it is possible to solve numerically the Cauchy problem for the linearisation of the general conformal field equations near spacelike infinity, which is only well-defined in Friedrich's cylinder picture. We have restricted ourselves here to the "core" of the equations - the spin-2 system - propagating on Minkowski space. We compute the numerical solutions for various classes of initial data, do convergence tests and also compare to exact solutions. We also choose initial data which intentionally violate the smoothness conditions and then check the analytical predictions about singularities. This paper is the first step in a long-term investigation of the use of conformal methods in numerical relativity.