Generalized Galilean algebras and Newtonian gravity

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• 作者：N. Gonzá ; lez^b ; ^{nicolas.gonzalez@physik.uni-muenchen.de" class="auth_mail" title="E-mail the corresponding author} ; G. Rubio^a ; ^{gurubio@udec.cl" class="auth_mail" title="E-mail the corresponding author} ; P. Salgado^a ; ^{pasalgad@udec.cl" class="auth_mail" title="E-mail the corresponding author} ; S. Salgado^a ; ^{sesalgado@udec.cl" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Physics Letters B
• 出版年：2016
• 出版时间：10 April 2016
• 年：2016
• 卷：755
• 期：Complete
• 页码：433-438
• 全文大小：299 K

文摘

The non-relativistic versions of the generalized Poincaré algebras and generalized AdS  -Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GB_n$\mathcal{G}{\mathfrak{B}}_n$ and GL_n$\mathcal{G}{\mathfrak{L}}_n$ respectively. Using a generalized Inönü–Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S  -expansion procedure allows us to find the GB₅$\mathcal{G}{\mathfrak{B}}_5$ algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic 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.