Massless collisionless matter is described in general relativity by the massless Einstein–Vlasov system. Given asymptotically flat Cauchy data for this system which is sufficiently close, in a suitable sense, to the trivial solution, Minkowski space, the resulting maximal development exists globally in time and asymptotically decays appropriately. This can be shown via a reduction to the corresponding result for the vacuum Einstein equations, a monumental result first obtained by Christodoulou–Klainerman in the early ’90s. A key step in the proof is to estimate certain Jacobi fields on the mass shell, a submanifold of the tangent bundle of the spacetime endowed with the Sasaki metric.