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

摘要

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 L~2 with a rate of O(Δ t~2 + h~m/Δt), when the exact solution belongs to H~m.