Convex regions of stationary spacetimes and Randers spaces. Applications to lensing and asymptotic flatness

Abstract

By using Stationary-to-Randers correspondence (SRC), a characterization of light and time-convexity of the boundary of a region of a standard stationary (n+1)-spacetime is obtained, in terms of the convexity of the boundary of a domain in a Finsler n or (n+1)-space of Randers type. The latter convexity is analyzed in depth and, as a consequence, the causal simplicity and the existence of causal geodesics confined in the region and connecting a point to a stationary line are characterized. Applications to asymptotically flat spacetimes include the light-convexity of stationary hypersurfaces which project in a spacelike section of an end onto a sphere of large radius, as well as the characterization of their time-convexity with natural physical interpretations. The lens effect of both light rays and freely falling massive particles with a finite lifetime, (i.e. the multiplicity of such connecting curves) is characterized in terms of the focalization of the geodesics in the underlying Randers manifolds.

AMSLaTex, 41 pages. v2 is a major revision: new discussions on physical applicability of the results, especially to asymptotically flat spacetimes; references added

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Cited by in corpus (9)

• Gravitational lensing in the Kerr-Randers optical geometry
• Classical Lagrangians and Finsler structures for the nonminimal fermion sector of the Standard-Model Extension
• Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions
• Wind Finslerian structures: from Zermelo's navigation to the causality of spacetimes
• Equivalence of Gibbons-Werner method to geodesics method in the study of gravitational lensing
• On Finsler spacetimes with a timelike Killing vector field
• Light bending in a two black hole metric
• Can we make a Finsler metric complete by a trivial projective change?
• Riemannian manifolds dual to static spacetimes