Tidal effects away from the equatorial plane in Kerr backgrounds

Abstract: We study tidal effects on self-gravitating Newtonian stars rotating around a Kerr black hole in stable circular orbits away from the equatorial plane. Such cases are exemplified by a non-vanishing Carter's constant. Here, we calculate the tidal disruption limit (Roche limit) of the star numerically, in Fermi normal coordinates. The Roche limit is found to depend strongly on the choice of the orbit, and differs significantly from the equatorial plane result as one approaches nearly polar orbits. As expected, this difference is large when the star is close to the black hole (near to the innermost stable circular orbit) and becomes smaller when the star is far from it. We also discuss the dependence of the Roche limit on the equation of state of the star, taking two specific parameter values as examples.