Conformal and projective symmetries in Newtonian cosmology
arXiv:1605.00231 · doi:10.1016/j.geomphys.2016.11.012
Abstract
Definitions of non-relativistic conformal transformations are considered both in the Newton-Cartan and in the Kaluza-Klein-type Eisenhart/Bargmann geometrical frameworks. The symmetry groups that come into play are exemplified by the cosmological, and also the Newton-Hooke solutions of Newton's gravitational field equations. It is shown, in particular, that the maximal symmetry group of the standard cosmological model is isomorphic to the 13-dimensional conformal-Newton-Cartan group whose conformal-Bargmann extension is explicitly worked out. Attention is drawn to the appearance of independent space and time dilations, in contrast with the Schr{ö}dinger group or the Conformal Galilei Algebra.
LaTeX, 26 pages. Published version
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- Non-relativistic gravity theories in four spacetime dimensions
- Non-Lorentzian Supergravity and Kinematical Superalgebras
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