  ?In this work, we study the orbital stability of stationary solutions to the
relativistic Vlasov-Manev system. This system is a kinetic model describing the
evolution of a stellar system subject to its own gravity with some relativistic
corrections. For this system, the orbital stability was proved for isotropic
models constructed as minimizers of the Hamiltonian under a subcritical
condition. We obtain here this stability for all isotropic models by a
non-variationnal approach. We use here a new method developed in [23] for the
classical Vlasov-Poisson system. We derive the stability from the monotonicity
of the Hamiltonian under suitable generalized symmetric rearrangements and from
a Antonov type coer- civity property. We overcome here two new difficulties :
the first one is the a priori non-continuity of the potentials, from which a
greater control of the re- arrangements is necessary. The second difficulty is
related to the homogeneity breaking which does not give the boundedness of the
kinetic energy. Indeed, in this paper, we does not suppose any subcritical
condition satisfied by the steady states.
