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arXiv · 2007.00983

Hamiltonian dynamics of doubly-foliable space-times

Cecília Gergely·Zoltán Keresztes·László Árpád Gergely
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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.

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Cecília Gergely, Zoltán Keresztes, László Árpád Gergely. 2020-07-02. Hamiltonian dynamics of doubly-foliable space-times. https://doi.org/10.3390/universe4010009

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