Proof of the Thin Sandwich Conjecture

TL;DR

This paper proves the validity of the Thin Sandwich Conjecture in general relativity under specific geometric conditions, impacting the understanding of Einstein's evolution equations and superspace.

Contribution

It establishes the conditions under which the Thin Sandwich Conjecture holds, providing a rigorous proof within a defined subset of initial data.

Findings

The conjecture is valid under certain geometric conditions.

The conditions define an open but non-generic set of data.

Implications for the superspace picture are discussed.

Abstract

We prove that the Thin Sandwich Conjecture in general relativity is valid, provided that the data $(g_{ab},\dot g_{ab})$ satisfy certain geometric conditions. These conditions define an open set in the class of possible data, but are not generically satisfied. The implications for the ``superspace'' picture of the Einstein evolution equations are discussed.