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

Abstract

In this paper, we demonstrate for the first time that it is possible to solve numerically the Cauchy problem for the linearization of the general conformal field equations near space-like 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, perform convergence tests and also compare with the 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. © 2012 IOP Publishing Ltd.