What is the explicit of vertical epicyclic frequency in Schwarzschild and Kerr spacetime outside of the equatorial plane?

12 March 2020 1 382 Report

I am interested in studying the vertical epicyclic frequencies in Schwarzschild and Kerr metrics in the whole 3D space, not only in the equatorial plane. I have looked up in the literature and I have found the explicit expression of such frequency only in the equatorial plane. Could someone please tell me the correct formula outside the equatorial plane?

Thank you in advance for your help!

Nelson Velandia

There is a paper which works the frequency from Hamiltonian formalism

Article Hamiltonian of a spinning test-particle in curved spacetime

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