Mechanics and Newton-Cartan-Like Gravity on the Newton-Hooke Space-time

Abstract

We focus on the dynamical aspects of Newton-Hooke space-time ${\mathcal{N}\mathcal{H}}_{+}$ mainly from the viewpoint of geometric contraction of the de Sitter spacetime. We first discuss the Newton-Hooke classical mechanics, especially the continuous medium mechanics, in this framework. Then, we establish a consistent theory of gravity on the Newton-Hooke space-time as a kind of Newton-Cartan-like theory, parallel to the Newton's gravity in the Galilei space-time. Finally, we give the Newton-Hooke invariant Schrödinger equation from the geometric contraction, where we can relate the conservative probability in some sense to the mass density in the Newton-Hooke continuous medium mechanics. Similar consideration may apply to the Newton-Hooke space-time ${\mathcal{N}\mathcal{H}}_{-}$ contracted from anti-de Sitter spacetime.

21 pages, 1 figure, revtex4; version to appear in PRD

References in corpus (1)

• On de Sitter Invariant Special Relativity and Cosmological Constant as Origin of Inertia

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