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

Bechouche, Philippe; Besse, Nicolas

ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 3, pp. 573-595.

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 $𝒪$ (Δt² + h^m/Δt), when the exact solution belongs to H^m.

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