PoS - Proceedings of Science
Volume 329 - International Conference on Black Holes as Cosmic Batteries: UHECRs and Multimessenger Astronomy (BHCB2018) - Main session
Degenerate metrics on a dual geometry of spherically symmetric space-time
A.C. Lucizani*, L.A. Cabral, P.T. Seidel and A.J. Capistrano
Full text: pdf
Pre-published on: May 13, 2019
Published on: May 21, 2019
We consider a massive spinless particle in a particular curved space-time described by a phase space formalism. For this space-time, we determine nontrivial conserved quantities and geometrical invariants by analytical and numerical methods. By analytic calculations, we revisit (perform) a method to relate two kinds of geometries associated with conserved quantities, whose dual metrics are constructed. The method relies on the calculation of the Stackel-Killing tensors (SKT) presented in a spherically symmetric space-time. We have a system of partial differential equations (PDE) for the symmetric components of the SKT obtained for a given space-time metric. We note that the PDE system is highly non-trivial according to the isometry structure of the original metric. A degenerate metric solution appears in the dual structure, and it is compared with recent works involving spacetime-bridge solutions in vacuum gravity and nontrivial extensions of the Schwarzschild spacetime.
DOI: https://doi.org/10.22323/1.329.0003
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