A mechanism for a "leaky" black hole to catalyze galaxy formation

In the gravitational field of a Schwarzschild-like black hole, particles infalling from rest at infinity, and black hole "wind" particles with relativistic velocity leaking radially out from the nominal horizon, both have the same magnitude of velocity at any radius from the hole. Hence when equally massive infalling and wind particles collide at any radius, they yield collision products with zero center of mass radial velocity, which can then nucleate star formation at the collision radius. We suggest that this gives a mechanism by which a central black hole can catalyze galaxy formation. For disk galaxies, this mechanism explains the observed approximately exponential falloff of the surface brightness with radius, and gives an estimate of the associated scale length.