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 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.

28 pages, 7 figures, final version as published in Class. Quant. Grav

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• An exact smooth Gowdy-symmetric generalized Taub-NUT solution
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• COFFEE -- An MPI-parallelized Python package for the numerical evolution of differential equations
• The Spin-2 Equation on Minkowski Background
• Fully pseudospectral solution of the conformally invariant wave equation on a Kerr background
• Explorations of the infinite regions of space-time
• Criticality of inhomogeneous Nariai-like cosmological models
• The chart based approach to studying the global structure of a spacetime induces a coordinate invariant boundary
• Numerical Brill-Lindquist initial data with a Schwarzschildean end at spatial infinity
• The characteristic initial value problem for the conformally invariant wave equation on a Schwarzschild background
• The space spinor formalism and estimates for spinor fields