Tidal interaction of a small black hole in the field of a large Kerr black hole

TL;DR

This paper calculates how a small black hole's mass and angular momentum change due to tidal forces from a larger Kerr black hole, considering relativistic circular orbits up to the innermost stable orbit.

Contribution

It provides leading-order calculations of tidal interaction rates for a small black hole in the field of a large Kerr black hole, including relativistic effects and all orbital velocities below the innermost stable orbit.

Findings

Rates depend only on the orbital velocity at the innermost stable orbit as it approaches V_{isco}.

The calculated rates are valid for all relativistic circular orbits below the innermost stable orbit.

The results are independent of the large black hole's spin parameter near the innermost stable orbit.

Abstract

The rates at which the mass and angular momentum of a small black hole change as a result of a tidal interaction with a much larger black hole are calculated to leading order in the small mass ratio. The small black hole is either rotating or nonrotating, and it moves on a circular orbit in the equatorial plane of the large Kerr black hole. The orbits are fully relativistic, and the rates are computed to all orders in the orbital velocity V < V_{isco}, which is limited only by the size of the innermost stable circular orbit. We show that as V \to V_{isco}, the rates take on a limiting value that depends only on V_{isco} and not on the spin parameter of the large black hole.