The Hubble stream near a massive object: the exact analytical solution for the spherically-symmetric case

The gravitational field of a massive object (for instance, of a galaxy group or cluster) disturbs the Hubble stream, decreasing its speed. Dependence $v(r_0)$ of the radial velocity of the stream from the present-day radius $r_0$ can be directly observed and may provide valuable information about the cluster properties. We offer an exact analytical relationship $v(r_0)$ for a spherically-symmetric system.