Generalized Galilean algebras and Newtonian gravity

Abstract The non-relativistic versions of the generalized Poincare 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 G B n and G L n respectively. Using a generalized Inonu–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 G 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.