Proper time for polar and equatorial orbits in Kerr metric

[dman12]

Hi. I've been struggling with a formulation of the twin paradox in the Kerr metric.

Imagine there are two twins at some radius in a Kerr metric. One performs equatorial circular motion whilst the other performs polar circular motion. They separate from one another and the parameters of the motion are such that they meet again when the polar twin next crosses the equatorial plane (ie having traveled through theta=pi). I'm trying to calculate the proper time elapsed for both twins in this case.

I can work out the proper time for the equatorial twin by solving the equations of motion from a Lagrangian for the Kerr metric but am finding it difficult to work out proper times for the polar orbit?

Any help would be much appreciated!

 

[Mentz114]

I recall that this old paper discusses the polar and equatorial orbits in Kerr spacetime. It might be be helpful

arXiv:gr-qc/0202090v1 26 Feb 2002 (http://arxiv.org/abs/gr-qc/0202090v1)