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Hamiltonian Dynamics of Doubly-Foliable Space-Times

Institute of Physics, University of Szeged, 6720 Szeged, Hungary
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Universe 2018, 4(1), 9; https://doi.org/10.3390/universe4010009
Received: 1 November 2017 / Revised: 15 December 2017 / Accepted: 18 December 2017 / Published: 3 January 2018
The 2 + 1 + 1 decomposition of space-time is useful in monitoring the temporal evolution of gravitational perturbations/waves in space-times with a spatial direction singled-out by symmetries. Such an approach based on a perpendicular double foliation has been employed in the framework of dark matter and dark energy-motivated scalar-tensor gravitational theories for the discussion of the odd sector perturbations of spherically-symmetric gravity. For the even sector, however, the perpendicularity has to be suppressed in order to allow for suitable gauge freedom, recovering the 10th metric variable. The 2 + 1 + 1 decomposition of the Einstein–Hilbert action leads to the identification of the canonical pairs, the Hamiltonian and momentum constraints. Hamiltonian dynamics is then derived via Poisson brackets. View Full-Text
Keywords: space-time foliation; extrinsic curvature; normal fundamental form and scalar; symmetries; geometrodynamics space-time foliation; extrinsic curvature; normal fundamental form and scalar; symmetries; geometrodynamics
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Gergely, C.; Keresztes, Z.; Gergely, L.Á. Hamiltonian Dynamics of Doubly-Foliable Space-Times. Universe 2018, 4, 9.

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