Gravitomagnetic dynamical friction

TL;DR

This paper introduces the concept of gravitomagnetic dynamical friction, a relativistic effect where a spinning black hole experiences a new force due to its spin interacting with surrounding stars, causing precession and spin-orbit coupling.

Contribution

It calculates the magnitude of gravitomagnetic dynamical friction for spinning black holes moving through stellar fields, incorporating spin-orbit coupling effects using post-Newtonian equations.

Findings

The effect causes black holes to spiral around their spin axis.

It exerts a torque leading to precession of the black hole's orbit.

The effect is negligible in most nonrelativistic astrophysical systems.

Abstract

A supermassive black hole moving through a field of stars will gravitationally scatter the stars, inducing a backreaction force on the black hole known as dynamical friction. In Newtonian gravity, the axisymmetry of the system about the black hole's velocity $\mathbf{v}$ implies that the dynamical friction must be anti-parallel to $\mathbf{v}$. However, in general relativity the black hole's spin $\mathbf{S}$ need not be parallel to $\mathbf{v}$, breaking the axisymmetry of the system and generating a new component of dynamical friction similar to the Lorentz force $\mathbf{F} = q\mathbf{v} \times \mathbf{B}$ experienced by a particle with charge $q$ moving in a magnetic field $\mathbf{B}$. We call this new force gravitomagnetic dynamical friction and calculate its magnitude for a spinning black hole moving through a field of stars with Maxwellian velocity dispersion $\sigma$, assuming that both $v$ and $\sigma$ are much less than the speed of light $c$. We use post-Newtonian equations of motion accurate to $\mathcal{O}(v^3/c^3)$ needed to capture the effect of spin-orbit coupling and also include direct stellar capture by the black hole's event horizon. Gravitomagnetic dynamical friction will cause a black hole with uniform speed to spiral about the direction of its spin, similar to a charged particle spiraling about a magnetic field line, and will exert a torque on a supermassive black hole orbiting a galactic center, causing the angular momentum of this orbit to slowly precess about the black-hole spin. As this effect is suppressed by a factor $(\sigma/c)^2$ in nonrelativistic systems, we expect it to be negligible in most astrophysical contexts but provide this calculation for its theoretical interest and potential application to relativistic systems.