Well-Posed Initial-Boundary Evolution in General Relativity

TL;DR

This paper demonstrates a well-posed initial-boundary value formulation for Einstein's equations using maximally dissipative boundary conditions, with a stable nonlinear evolution code and applications to gravitational waveform computation.

Contribution

It introduces a well-posed initial-boundary value problem for Einstein's equations in harmonic coordinates with a stable numerical implementation.

Findings

The nonlinear evolution code converges and is robustly stable.

The linearized version matches a characteristic code for waveform extraction.

Boundary conditions ensure well-posedness for small boundary data.

Abstract

Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in a linearized sense. The method is implemented as a nonlinear evolution code which satisfies convergence tests in the nonlinear regime and is robustly stable in the weak field regime. A linearized version has been stably matched to a characteristic code to compute the gravitational waveform radiated to infinity.