Nonexistence of an integral of the 6th degree in momenta for the Zipoy-Voorhees metric

Abstract

We prove nonexistence of a nontrivial integral that is polynomial in momenta of degree less than 7 for the Zipoy-Voorhees spacetime with the parameter $\delta =2$

7 pages, no figures

References in corpus (5)

• Towards adiabatic waveforms for inspiral into Kerr black holes: II. Dynamical sources and generic orbits
• Invariant characterization of Liouville metrics and polynomial integrals
• Spacetime Encodings II - Pictures of Integrability
• Spacetime Encodings I- A Spacetime Reconstruction Problem
• Carter-like constants of the motion in Newtonian gravity and electrodynamics

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