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

TL;DR

This paper develops and analyzes a second order wave equation system for linearized gravitational fields near infinity, demonstrating equivalence with first order systems and exploring numerical advantages in a conformal geometric setting.

Contribution

It derives a second order wave system for spin-2 fields near infinity and proves its solution space matches the first order system, highlighting potential numerical benefits.

Findings

Second order wave system is equivalent to first order system with proper data

Analysis shows differences and advantages of second order approach

Application in conformal geometry 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.