Static Solutions of the Vlasov-Einstein System

Static solutions of the SO(3)-symmetric Vlasov-Einstein system are studied via a variational approach. For the constitutive relation of the Emden-Fowler type φ(E,F)≡E ^{σ+ 1} F ^k we prove the existence of such solutions of sufficiently small mass-energy, provided 0<σ < k+3/2. These solutions are local minimizers of the energy-Casimir functional, subjected to a variational barrier. Accepted July 16, 2000?Published online January 22, 2001