On plane gravitational waves in real connection variables

Details On plane gravitational waves in real connection variables On plane gravitational waves in real connection variables

2010-06-21

arxiv.org/abs/1006.4146v2

Phys.Rev.D83:044034,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

v2: Matches published version, up to minor stylistic changes

Scientific paper

10.1103/PhysRevD.83.044034

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. Due to 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 non-local brackets, analogous to those of self-dual fields, for the triad variables chosen in this approach.

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