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Effective dynamics for Boson stars. (English) Zbl 1124.35084

The pseudo-relativistic Hartree equation describing boson stars under the influence of an external gravitational field is analyzed. The authors study the long time effective dynamics of solutions close to solitary waves, and they establish a long time stability result for solutions describing boson stars that move under the influence of a gravitational field. The proof of their main result tackles difficulties that are absent when deriving similar results on effective solitary wave motions for nonlinear Schrödinger or nonlinear wave equations. This is due to the fact that the pseudo-relativistic Hartree equation does not exhibit Galilean or Lorentz covariance.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
85A05 Galactic and stellar dynamics
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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