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In some recent papers, the relations existing between the metric propertiesof Randers spaces and the conformal geometry of stationary Lorentzian manifoldswere discovered and investigated. In this note, we focus on the equalitybetween the index of a geodesic in a Randers space and that of its lightlikelift in the associated conformal stationary spacetime. Moreover we make someremarks about regularity of the energy functional of a Finsler metric on theinfinite dimensional manifold of $H^1$ curves between two points, in connectionwith infinite dimensional techniques in Morse Theory.

The index of a geodesic in a Randers space and some remarks about the lack of regularity of the energy functional of a Finsler metric