A Kucha\v{r} Hypertime Formalism For Cylindrically Symmetric Spacetimes With Interacting Scalar Fields

TL;DR

This paper extends Kuchař's canonical transformation to cylindrically symmetric spacetimes with interacting scalar fields, enabling a Schrödinger-like formulation of their dynamics despite complex constraints.

Contribution

It applies Kuchař's formalism to non-vacuum cylindrically symmetric models with scalar fields, solving the constraints for a hypertime functional Schrödinger equation.

Findings

Constraints can be solved for momenta conjugate to embedding variables.

Dynamics can be expressed in a form suitable for a Schrödinger equation.

Formalism accommodates interacting scalar fields in cylindrical symmetry.

Abstract

The Kucha\v{r} canonical transformation for vacuum geometrodynamics in the presence of cylindrical symmetry is applied to a general non-vacuum case. The resulting constraints are highly non-linear and non-local in the momenta conjugate to the Kucha\v{r} 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.