Bohlin-Arnold-Vassiliev's duality and conserved quantities

Optical 2-metrics of Schwarzschild-Tangherlini Spacetimes and the Bohlin-Arnold Duality

We consider the projection of null geodesics of the Schwarzschild-Tangherlini metric in n+1 dimensions to the space of orbits of the static Killing vector where the motion of a given light ray is seen to lie in a plane. The projected curves coincide with the unparametrised geodesics of optical 2-metrics and can be equally understood as describing the motion of a non-relativistic particle in a central force. We consider a duality between the projected null curves for pairs of values of n and interpret its mathematical meaning in terms of the optical 2-metrics. The metrics are not projectively e…