Towards Loop Quantization of Plane Gravitational Waves

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.

14 pages

References in corpus (10)

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Cited by in corpus (10)

• Introduction to Loop Quantum Cosmology
• Covariance in self dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems
• Propagation of quantum gravity-modified gravitational waves on a classical FLRW spacetime
• Modifications to Gravitational Wave Equation from Canonical Quantum Gravity
• Classical axisymmetric gravity in real Ashtekar variables
• Canonical LQG operators and kinematical states for plane gravitational waves
• Emergent modified gravity: Polarized Gowdy model on a torus
• Aspects of Quantum Gravity Phenomenology and Astrophysics
• Quantum volume and length fluctuations in a midi-superspace model of Minkowski space
• Plane wave holonomies in loop quantum gravity II: sine wave solution