Spectral methods for the spin-2 equation near the cylinder at spatial infinity

TL;DR

This paper develops spectral numerical methods to solve the massless spin-2 equations near spatial infinity, enabling analysis of solutions at critical points where null infinity meets spatial infinity, and assesses their regularity.

Contribution

It introduces a spectral approach to numerically solve spin-2 equations near spatial infinity, providing insights into solution regularity at critical sets.

Findings

Successful numerical solutions up to critical sets

Spectral convergence rates reveal regularity properties

Enhanced understanding of spin-2 fields at spatial infinity

Abstract

We solve, numerically, the massless spin-2 equations, written in terms of a gauge based on the properties of conformal geodesics, in a neighbourhood of spatial infinity using spectral methods in both space and time. This strategy allows us to compute the solutions to these equations up to the critical sets where null infinity intersects with spatial infinity. Moreover, we use the convergence rates of the numerical solutions to read-off their regularity properties.