5 Stationary Asymptotically-Flat Solutions

Equilibrium states in galactic dynamics can be described as static or stationary solutions of the Einstein–Vlasov system, or of the Vlasov–Poisson system in the Newtonian case. Here we consider the relativistic case and we refer to the excellent review paper [141Jump To The Next Citation Point] for the Newtonian case. First, we discuss spherically-symmetric solutions for which the structure is quite well understood. On the other hand, almost nothing is known about the stability of the spherically-symmetric static solutions of the Einstein–Vlasov system, which is in sharp contrast to the situation for the Vlasov–Poisson system. At the end of this section a recent result [18Jump To The Next Citation Point] on axisymmetric static solutions will be presented.

 5.1 Existence of spherically-symmetric static solutions
 5.2 The structure of spherically-symmetric steady states
 5.3 Buchdahl-type inequalities
 5.4 Stability
 5.5 Existence of axisymmetric static solutions

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