Asymptotic behavior and orbital stability of galactic dynamics in relativistic scalar gravity

Details Asymptotic behavior and orbital stability of galactic dynamics in relativistic scalar gravity Asymptotic behavior and orbital stability of galactic dynamics in relativistic scalar gravity

2007-07-21

arxiv.org/abs/0707.3211v1

Physics

Mathematical Physics

30 pages, 3 figures

Scientific paper

10.1007/s00205-008-0173-x

The Nordstr\"om-Vlasov system is a relativistic Lorentz invariant generalization of the Vlasov-Poisson system in the gravitational case. The asymptotic behavior of solutions and the non-linear stability of steady states are investigated. It is shown that solutions of the Nordstr\"om-Vlasov system with energy grater or equal to the mass satisfy a dispersion estimate in terms of the conformal energy. When the energy is smaller than the mass, we prove existence and non-linear (orbital) stability of a class of static solutions (isotropic polytropes) against general perturbations. The proof of orbital stability is based on a variational problem associated to the minimization of the energy functional under suitable constraints.

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