# Tidal effects away from the equatorial plane in Kerr backgrounds

## TL;DR

This paper investigates how tidal disruption limits for stars in Kerr black hole orbits vary with orbital inclination, revealing significant differences from equatorial cases especially near the black hole.

## Contribution

It provides a numerical analysis of the Roche limit for stars in inclined Kerr orbits, highlighting the dependence on orbit type and stellar equation of state.

## Key findings

- Roche limit varies strongly with orbit inclination
- Significant differences from equatorial orbit results near the black hole
- Dependence on the star's equation of state is demonstrated

## 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.