Boundary conditions in linearized harmonic gravity

TL;DR

This paper addresses the initial-boundary value problem in linearized harmonic gravity, establishing well-posedness and developing stable computational algorithms for 3D bounded domains, with successful numerical tests.

Contribution

It introduces rigorous techniques for hyperbolic systems to ensure well-posedness and creates stable algorithms for Cauchy evolution in bounded domains in linearized gravity.

Findings

Numerical codes pass stability tests with random data.

Algorithms perform well with physical data.

Results applicable to plane and spherical boundaries.

Abstract

We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a set of six wave equations. The results are used to formulate computational algorithms for Cauchy evolution in a 3-dimensional bounded domain. Numerical codes based upon these algorithms are shown to satisfy tests of robust stability for random constraint violating initial data and random boundary data; and shown to give excellent performance for the evolution of typical physical data. The results are obtained for plane boundaries as well as piecewise cubic spherical boundaries cut out of a Cartesian grid.