Nonexistence of an integral of the 6th degree in momenta for the   Zipoy-Voorhees metric
  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 $\delta=2$ 
Boris S. Kruglikov and Vladimir S. Matveev
math-ph gr-qc math.DG math.MP