Collisionless black-hole capture

Collisionless matter approaching a black hole generally cannot dissipate enough orbital energy to remain bound, so direct capture requires sufficiently small angular momentum. For nonrelativistic incident speed $v$, a Schwarzschild black hole has direct test-particle capture cross-section approximately $16\pi G^2{M}^2/(c^2{v}^2)$. A Newtonian pericentre estimate using the Schwarzschild radius instead gives $4\pi G^2{M}^2/(c^2{v}^2)$. Both show that capture at a given mass density is suppressed by order $(v/c{)}^2$ relative to supersonic Bondi--Hoyle--Lyttleton accretion. Tidal disruption events provide a distinct way to accrete some stellar debris.