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International audienceWe 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 L 2 with a rate of $\mathcal{O}$ (Δt 2 + hm /Δt), when the exact solution belongs to Hm

Analysis of a semi-Lagrangian method for the spherically symmetric Vlasov-Einstein system