Type of Work
Physical Review D
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.
Hinterleitner, F. and Major, Seth, "Plane gravitational waves in real connection variables" (2011). Hamilton Digital Commons.
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