Geometrization of metric boundary data for Einstein's equations

TL;DR

This paper reformulates boundary conditions for Einstein's equations in a geometric form, advancing the development of well-posed initial boundary value problems in general relativity.

Contribution

It recasts Sommerfeld-type boundary conditions into a geometric form, facilitating their application to various metric formulations of Einstein's equations.

Findings

Boundary conditions are expressed geometrically.

A step towards broader application of boundary conditions.

Enhancement of well-posedness in Einstein's equations.

Abstract

The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A well-posed initial boundary value problem based upon a new formulation of constraint-preserving boundary conditions of the Sommerfeld type has recently been established for such systems. In this paper these boundary conditions are recast in a geometric form. This serves as a first step toward their application to other metric formulations of Einstein's equations.