Velocities and momenta in an extended elliptic form of the initial-value conditions

摘要

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.