CONSERVED QUANTITIES AND DUALITIES FOR PARTICLES IN CURVED SPACE-TIME

Abstract

We consider particles moving in curved space-time and associated symmetries. We use a generalized Killing equation and search for solutions involving Killing tensors associated with space-time metric. With these tensors some conserved quantities are constructed and they are valid along particles geodesic. In the Hamiltonian formalism for these particles, the conserved quantities can generate a dual description of the metric. We construct nontrivial dual metrics and consider a kind of geometric duality that involves a completely different space-time. From these metrics we calculate geometric invariants and examine the singularity structure of the dual space-time.