We consider the spherically symmetric Vlasov-Einstein system in the case of asymptotically flat spacetimes.
From the physical point of view this system of equations can model the formation of a spherical black hole by
gravitational collapse or describe the evolution of galaxies and globular clusters. We present high-order numerical schemes based on
semi-Lagrangian
techniques. The convergence of the solution of the discretized problem to
the exact solution is proven and high-order error estimates are supplied. More precisely the metric coefficients
converge in L∞ and the statistical distribution function of the matter and its moments converge in L2 with a rate of
$\mathcal{O}$
(Δt2 + hm/Δt), when the exact solution belongs to Hm.