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

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

2004-10-30

arxiv.org/abs/hep-th/0411004v2

Phys.Rev. D71 (2005) 044030

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1103/PhysRevD.71.044030

We focus on the dynamical aspects of Newton-Hooke space-time ${\cal NH}_+$ 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 Schr\"odinger 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 ${\cal NH}_-$ contracted from anti-de Sitter spacetime.

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