de Sitter geodesics: reappraising the notion of motion

Details de Sitter geodesics: reappraising the notion of motion de Sitter geodesics: reappraising the notion of motion

2011-10-05

arxiv.org/abs/1110.0965v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages. V2: Presentation changes aiming at clarifying the text; version accepted for publication in Gen. Rel. Grav

Scientific paper

10.1007/s10714-012-1338-3

The de Sitter spacetime is transitive under a combination of translations and proper conformal transformations. Its usual family of geodesics, however, does not take into account this property. As a consequence, there are points in de Sitter spacetime which cannot be joined to each other by any one of these geodesics. By taking into account the appropriate transitivity properties in the variational principle, a new family of maximizing trajectories is obtained, whose members are able to connect any two points of the de Sitter spacetime. These geodesics introduce a new notion of motion, given by a combination of translations and proper conformal transformations, which may possibly become important at very-high energies, where conformal symmetry plays a significant role.

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