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arXiv · hep-th/0411004

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

Yu Tian·Han-Ying Guo·Chao-Guang Huang·Zhan Xu·Bin Zhou
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Abstract

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 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 ${\cal NH}_-$ contracted from anti-de Sitter spacetime.

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Yu Tian, Han-Ying Guo, Chao-Guang Huang, Zhan Xu, Bin Zhou. 2005-02-27. Mechanics and Newton-Cartan-Like Gravity on the Newton-Hooke Space-time. https://doi.org/10.1103/physrevd.71.044030

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