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Towards Loop Quantization of Plane Gravitational Waves
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.Comment: 14 page