Kuchar-caron hypertime formalism for cylindrically symmetric spacetimes with interacting scalar fields.

Abstract

The Kucha\ifmmode \check{r}\else \v{r}\fi{} canonical transformation for vacuum geometrodynamics in the presence of cylindrical symmetry is applied to a general nonvacuum case. The resulting constraints are highly nonlinear and nonlocal in the momenta conjugate to the Kucha\ifmmode \check{r}\else \v{r}\fi{} embedding variables. However, it is demonstrated that the constraints can be solved for these momenta and thus the dynamics of cylindrically symmetric models can be cast in a form suitable for the construction of a hypertime functional Schr\"odinger equation.