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Universe 2018, 4(1), 9; https://doi.org/10.3390/universe4010009

Hamiltonian Dynamics of Doubly-Foliable Space-Times

Institute of Physics, University of Szeged, 6720 Szeged, Hungary
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Received: 1 November 2017 / Revised: 15 December 2017 / Accepted: 18 December 2017 / Published: 3 January 2018
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Abstract

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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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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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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