Killing tensors in stationary and axially symmetric space-times
arXiv:1602.08968 · doi:10.1016/j.geomphys.2016.09.009
Abstract
We discuss the existence of Killing tensors for certain (physically motivated) stationary and axially symmetric vacuum space-times. We show nonexistence of a nontrivial Killing tensor for a Tomimatsu-Sato metric (up to valence 7), for a C-metric (up to valence 9) and for a Zipoy-Voorhees metric (up to valence 11). The results are obtained by mathematically completely rigorous, nontrivial computer algebra computations with a huge number of equations involved in the problem.
References in corpus (6)
- Interpreting the C-metric
- The non-integrability of the Zipoy-Voorhees metric
- Spacetime Encodings II - Pictures of Integrability
- The geodesic flow of a generic metric does not admit nontrivial integrals polynomial in momenta
- On integrability of certain rank 2 sub-Riemannian structures
- Reducibility of Valence-3 Killing Tensors in Weyl's Class of Stationary and Axially Symmetric Space-Times