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Equilibrium states in galactic dynamics can be described as stationarysolutions of the Vlasov-Poisson system, which is the non-relativistic case, orof the Vlasov-Einstein system, which is the relativistic case. To obtainspherically symmetric stationary solutions the distribution function of theparticles (stars) on phase space is taken to be a function of the particleenergy and angular momentum. We give a new condition on this function whichguarantees that the resulting steady state has finite mass and compact supportboth for the non-relativistic and the relativistic case. The condition is localin the sense that only the asymptotic behaviour for energy values close to themaximal energy value in the particle distribution needs to be prescribed.Comment: 23 pages LaTeX2

Compact support of spherically symmetric equilibria in non-relativistic and relativistic galactic dynamics