Cauchy boundaries in linearized gravitational theory

TL;DR

This paper examines the numerical stability of linearized gravitational equations in a bounded domain, proposing criteria and testing various boundary algorithms to ensure robust stability in simulations.

Contribution

It introduces a stability testbed and demonstrates the robustness of a specific evolution-boundary algorithm for linearized gravity.

Findings

The stability criteria effectively evaluate boundary algorithms.

A finite difference code was developed for 3+1 linearized Einstein equations.

The algorithm showed robust stability with random initial and boundary data.

Abstract

We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a 3-dimensional bounded domain. Criteria of robust stability are proposed, developed into a testbed and used to study various evolution-boundary algorithms. We construct a standard explicit finite difference code which solves the unconstrained linearized Einstein equations in the 3+1 formulation and measure its stability properties under Dirichlet, Neumann and Sommerfeld boundary conditions. We demonstrate the robust stability of a specific evolution-boundary algorithm under random constraint violating initial data and random boundary data.