The Generalized Thin-Sandwich Problem and its Local Solvability

TL;DR

This paper investigates the conditions under which a specified initial configuration of fields in Einstein gravity coupled with matter uniquely determines a solution, establishing criteria for local solvability of the generalized thin-sandwich problem.

Contribution

It provides new sufficient conditions for the local solvability of the generalized thin-sandwich problem in Einstein gravity with matter fields.

Findings

Established criteria for local solvability.

Extended the thin-sandwich problem to include matter fields.

Provided conditions applicable to gauge and scalar fields.

Abstract

We consider Einstein Gravity coupled to dynamical matter consisting of a gauge field with any compact gauge group and minimally coupled scalar fields. We investigate the conditions under which a free specification of a spatial field configuration for the total system and its derivative with respect to coordinate-time determines a solution to the field equations (generalized thin-sandwich problem). Sufficient conditions for local solvability (in the space of fields) are established.