Geodesics on convex regions of stationary spacetimes and Finslerian Randers spaces

Details Geodesics on convex regions of stationary spacetimes and Finslerian Randers spaces Geodesics on convex regions of stationary spacetimes and Finslerian Randers spaces

2011-12-16

arxiv.org/abs/1112.3892v1

Mathematics

Differential Geometry

AMSLaTex, 31 pages

Scientific paper

By using Stationary-to-Randers correspondence (SRC), a characterization of light/time-convexity of the boundary of a region of a standard stationary spacetime is obtained, in terms of the convexity of the boundary of a domain in a Finsler space of Randers type. The latter is also analyzed in depth and, as a consequence, the existence of geodesics connecting a point and a stationary line by means of lightlike and timelike geodesics is fully characterized in terms of both, Finslerian and causal elements. Applications to asymptotically flat spacetimes include the light-convexity but non time-convexity of large asymptotic balls, with natural physical interpretations. Topological lensing effects for both, light rays and freely falling massive particles with a finite lifetime, are pointed out. A revision of the causal and variational tools used in this type of problems from the viewpoint of SRC is also carried out.

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