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arXiv · 1604.06313

Generalized Galilean Algebras and Newtonian Gravity

N. L. González Albornoz·G. Rubio·P. Salgado·S. Salgado
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Abstract

The non-relativistic versions of the generalized Poincar\'{e} algebras and generalized $AdS$-Lorentz algebras are obtained. This non-relativistic algebras are called, generalized Galilean algebras type I and type II and denoted by $\mathcal{G}\mathfrak{B}_{n}$ and $\mathcal{G}\mathfrak{L}_{_{n}}$ respectively. Using a generalized In\"{o}n\"{u}--Wigner contraction procedure we find that the generalized Galilean algebras type I can be obtained from the generalized Galilean algebras type II. The $S$-expansion procedure allows us to find the $\mathcal{G}\mathfrak{B}_{_{5}}$ algebra from the Newton--Hooke algebra with central extension. The procedure developed in Ref. \cite{newton} allow us to show that the non-relativistic limit of the five dimensional Einstein--Chern--Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.

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N. L. González Albornoz, G. Rubio, P. Salgado, S. Salgado. 2016-04-21. Generalized Galilean Algebras and Newtonian Gravity. https://doi.org/10.1016/j.physletb.2016.02.037

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