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By using Stationary-to-Randers correspondence (SRC), a characterization oflight 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 adomain in a Finsler n or (n+1)-space of Randers type. The latter convexity isanalyzed in depth and, as a consequence, the causal simplicity and theexistence of causal geodesics confined in the region and connecting a point toa stationary line are characterized. Applications to asymptotically flatspacetimes include the light-convexity of stationary hypersurfaces whichproject in a spacelike section of an end onto a sphere of large radius, as wellas the characterization of their time-convexity with natural physicalinterpretations. The lens effect of both light rays and freely falling massiveparticles with a finite lifetime, (i.e. the multiplicity of such connectingcurves) is characterized in terms of the focalization of the geodesics in theunderlying Randers manifolds.

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