Killing tensors in stationary and axially symmetric space-times
Andreas Vollmer
TL;DR
This paper investigates the existence of Killing tensors in specific stationary, axially symmetric vacuum space-times, using rigorous computer algebra to establish nonexistence results up to certain tensor valences.
Contribution
It provides the first rigorous nonexistence proofs of Killing tensors in these space-times for valences up to 11, advancing understanding of spacetime symmetries.
Findings
No nontrivial Killing tensor exists for Tomimatsu-Sato up to valence 7.
No nontrivial Killing tensor exists for C-metric up to valence 9.
No nontrivial Killing tensor exists for Zipoy-Voorhees up to valence 11.
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.
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