The second order spin-2 system in flat space near space-like and null-infinity

Abstract

In previous work, the numerical solution of the linearized gravitational field equations near space-like and null-infinity was discussed in the form of the spin-2 zero-rest-mass equation for the perturbations of the conformal Weyl curvature. The motivation was to study the behavior of the field and properties of the numerical evolution of the system near infinity using Friedrich's conformal representation of space-like infinity as a cylinder. It has been pointed out by H.O. Kreiss and others that the numerical evolution of a system using second order wave equations has several advantages compared to a system of first order equations. Therefore, in the present paper we derive a system of second order wave equations and prove that the solution spaces of the two systems are the same if appropriate initial and boundary data are given. We study the properties of this system of coupled wave equations in the same geometric setting and discuss the differences between the two approaches.

19 pages, 7 figures, updated version agrees with the published version

References in corpus (5)

• New, efficient, and accurate high order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions
• A multi-block infrastructure for three-dimensional time-dependent numerical relativity
• Multi-block simulations in general relativity: high order discretizations, numerical stability, and applications
• Numerical space-times near space-like and null infinity. The spin-2 system on Minkowski space
• Polyhomogeneous expansions close to null and spatial infinity

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• Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity
• Numerical construction of initial data for Einstein's equations with static extension to space-like infinity
• Spectral methods for the spin-2 equation near the cylinder at spatial infinity
• Fully pseudospectral solution of the conformally invariant wave equation on a Kerr background
• Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. III: Nonspherical Schwarzschild waves and singularities at null infinity
• Explorations of the infinite regions of space-time
• Numerical Brill-Lindquist initial data with a Schwarzschildean end at spatial infinity
• The space spinor formalism and estimates for spinor fields
• The characteristic initial value problem for the conformally invariant wave equation on a Schwarzschild background