Accretion of Dark Matter onto a Moving Schwarzschild Black Hole: An Exact Solution

TL;DR

This paper derives an exact stationary solution for dark matter accretion onto a moving Schwarzschild black hole, revealing how the accretion rate varies with black hole velocity and gas temperature, relevant for primordial black hole growth.

Contribution

It provides the first exact solution for collisionless dark matter accretion onto a moving black hole, including a formula for the mass accretion rate.

Findings

Accretion rate is generally nonmonotonic with black hole velocity.

High gas temperatures lead to a monotonic accretion rate proportional to the Lorentz factor.

The results are applicable to primordial black hole growth in the early Universe.

Abstract

We investigate accretion of dark matter onto a moving Schwarzschild black hole. The dark matter is modeled by the collisionless Vlasov gas, assumed to be in thermal equilibrium at infinity. We derive an exact stationary solution and provide a compact formula for the mass accretion rate. In general, the mass accretion rate is a nonmonotonic function of the black hole velocity. A monotonic relation (the accretion rate proportional to the Lorentz factor associated with the velocity of the black hole) is obtained for high asymptotic temperatures of the gas. The derived accretion rates are relevant for the growth of primordial black holes in the early Universe.