Velocities and Momenta in an Extended Elliptic Form of the Initial Value Conditions

TL;DR

This paper extends the conformal structure of initial value constraints in general relativity to include various mean curvature foliations, demonstrating the approach using the momentum phase space without tensor decomposition.

Contribution

It introduces an extended conformal approach incorporating constant mean curvature conditions, simplifying the solution process in the initial value problem.

Findings

Extended the conformal structure to include mean curvature foliations

Demonstrated equivalence with the conformal thin sandwich approach

Avoided tensor decomposition in solving the equations

Abstract

The complete form of the constraints following from their conformal structure is extended so as to include constant mean curvature and other mean curvature foliations. This step is demonstrated using the momentum phase space approach. This approach yields equations of exactly the same form as the extended conformal thin sandwich approach. In solving the equations, it is never necessary actually to perform a tensor decomposition.