Dualities and geometrical invariants for static and spherically symmetric spacetimes

Abstract

In this work, we consider spinless particles in curved spacetime and symmetries related to extended isometries. We search for solutions of a generalized Killing equation whose structure entails a general class of Killing tensors. The conserved quantities along particle’s geodesic are associated with a dual description of the spacetime metric. In the Hamiltonian formalism, some conserved quantities generate a dual description of the metric. The Killing tensors belonging to the conserved objects imply in a nontrivial class of dual metrics even for a Schwarzschild metric in the original spacetime. From these metrics, we construct geometrical invariants for classes of dual spacetimes to explore their singularity structure. A nontrivial singularity behavior is obtained in the dual sector.