Towards Loop Quantization of Plane Gravitational Waves

TL;DR

This paper advances the loop quantum gravity approach by formulating a quantization scheme for plane gravitational waves, specifically pp-waves, through a detailed analysis of the Gowdy model and its constraints.

Contribution

It introduces a method to include Killing equations in the Gowdy model, enabling loop quantization of plane-fronted gravitational waves with parallel rays.

Findings

Constraint algebra forms a set of first-class constraints.

Constraints are expressed in terms of classical quantities with quantum operator equivalents.

The approach makes space-times with pp-waves accessible to loop quantum gravity techniques.

Abstract

The polarized Gowdy model in terms of Ashtekar-Barbero variables is further reduced by including the Killing equations for plane-fronted parallel gravitational waves with parallel rays. The resulting constraint algebra, including one constraint derived from the Killing equations in addition to the standard ones of General Relativity, are shown to form a set of first-class constraints. Using earlier work by Banerjee and Date the constraints are expressed in terms of classical quantities that have an operator equivalent in Loop Quantum Gravity, making space-times with pp-waves accessible to loop quantization techniques.