Problems which are well-posed in a generalized sense with applications to the Einstein equations

TL;DR

This paper demonstrates the well-posedness of boundary conditions for Einstein equations in harmonic form, using pseudo-differential theory, which benefits numerical relativity simulations.

Contribution

It introduces a generalized well-posedness framework for Einstein equations with constraint-preserving boundary conditions in second order form.

Findings

Established well-posedness of boundary conditions for Einstein equations

Used pseudo-differential theory for systems in generalized sense

Boundary conditions are suitable for numerical calculations

Abstract

In the harmonic description of general relativity, the principle part of Einstein equations reduces to a constrained system of 10 curved space wave equations for the components of the space-time metric. We use the pseudo-differential theory of systems which are well-posed in the generalized sense to establish the well-posedness of constraint preserving boundary conditions for this system when treated in second order differential form. The boundary conditions are of a generalized Sommerfeld type that is benevolent for numerical calculation.