Abstract
We investigate using plane-fronted gravitational wave space-times as model systems to study loop quantization techniques and dispersion relations. In this classical analysis we start with planar symmetric space-times in the real connection formulation. We reduce via Dirac constraint analysis to a final form with one canonical pair and one constraint, equivalent to the metric and Einstein equations of plane-fronted-with-parallel-rays waves. Because of the symmetries and use of special coordinates, general covariance is broken. However, this allows us to simply express the constraints of the consistent system. A recursive construction of Dirac brackets results in nonlocal brackets, analogous to those of self-dual fields, for the triad variables. Not surprisingly, this classical analysis produces no evidence for dispersion, i.e. a variable propagation speed of gravitational plane-fronted-with-parallel-rays waves.
- Received 24 June 2010
DOI:https://doi.org/10.1103/PhysRevD.83.044034
© 2011 American Physical Society