Closed-Flux Solutions to the Constraints for Plane Gravity Waves

TL;DR

This paper develops solutions for plane gravitational waves in a quantum gravity framework using closed flux loops, ensuring the Gauss constraint is satisfied everywhere along the wave's propagation axis.

Contribution

It introduces closed flux loop solutions in the Hamiltonian quantization of plane gravitational waves, improving upon previous open flux line models.

Findings

Solutions satisfy the Gauss constraint at all points along the z axis.

Closed flux loop solutions are compatible with the Hamiltonian framework.

Advances the understanding of quantum plane gravitational waves.

Abstract

The metric for plane gravitational waves is quantized within the Hamiltonian framework, using a Dirac constraint quantization and the self-dual field variables proposed by Ashtekar. The z axis (direction of travel of the waves) is taken to be the entire real line rather than the torus (manifold coordinatized by (z,t) is RxR rather than $S_1$ x R). Solutions to the constraints proposed in a previous paper involve open-ended flux lines running along the entire z axis, rather than closed loops of flux; consequently, these solutions are annihilated by the Gauss constraint at interior points of the z axis, but not at the two boundary points. The solutions studied in the present paper are based on closed flux loops and satisfy the Gauss constraint for all z.