Effective Dynamics for Boson Stars
  We study solutions close to solitary waves of the pseudo-relativistic Hartree equation describing boson stars under the influence of an external gravitational field. In particular, we analyze the long-time effective dynamics of such solutions. In essence, we establish a (long-time) stability result for solutions describing boson stars that move under the influence of an external gravitational field. 
Juerg Froehlich, B. Lars G. Jonsson, Enno Lenzmann