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abstract: 'While there exist now formulations of initial boundary value problems for Einstein’s field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two different approaches we discuss how this difficulty arises under general assumptions. So far it is not known whether it can be overcome without imposing conditions on the geometry of the boundary. We point out a natural and important class of initial boundary value problems which may offer possibilities to arrive at a fully covariant formulation.'
author:
- |
    Helmut Friedrich\
    Max-Planck-Institut für Gravitationsphysik\
    Am Mühlenberg 1\
    14476 Golm, Germany
title: 'Initial boundary value problems for Einstein’s field equations and geometric uniqueness'
---

Introduction
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This article is concerned with the general principle of geometric uniqueness in the context of the initial boundary value problem for Einstein’s field equations. Because Jürgen Ehlers had always been attracted by problems of principle and he took a certain interest in the initial boundary value problem ([@ehlers:kind]) I devote this article to his memory.

The Cauchy problem for Einstein’s field equations has a long history ([@chrusciel:friedrich]). It was put on a solid basis when Choquet-Bruhat proved the first local existence 