references). In the present article we shall consider besides the formulation of [@friedrich:nagy] only the one proposed recently by Kreiss, Reula, Sarbach, and Winicour (cf. ([@kreiss:et:al:2009] and references to earlier work given there). It is based on a general and systematic analysis of well posed initial boundary value problems for systems of wave equations. Though the application to Einstein’s field equations is not completely analysed yet, the approach appears to be very flexible and it may offer chances to clarify a question which I consider a main open problem of the subject. While being pointed out at various occasions ([@friedrich:dpg], [@friedrich:nagy]) it has largely been ignored so far. Analysing in local evolution problems the preservation of constraints and gauge conditions is obviously a task which needs to be solved before geometric uniqueness can be addressed.

The space-time structures underlying the general theory of relativity are isometry classes of space-times. A general discussion of boundary value problems of some sort for Einstein’s field equations should thus produce solutions $g_{\mu \nu}$ which, considered as geometric objects, should not depend on any extraneous structures such as background metrics, frame fields, gauge source functions, gauge conditions, coordinates, etc. which are introduced to formulate suitable 