Killing tensors in stationary and axially symmetric space-times
Differential Geometry
2017-04-12 v1 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1602.08968,
title = {Killing tensors in stationary and axially symmetric space-times},
author = {Andreas Vollmer},
journal= {arXiv preprint arXiv:1602.08968},
year = {2017}
}