Gravitomagnetic dynamical friction

Understand

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 $c$.