Self-similar spherically symmetric solutions of the massless Einstein-Vlasov system

We construct the general spherically symmetric and self-similar solution of the Einstein-Vlasov system (collisionless matter coupled to general relativity) with massless particles, under certain regularity conditions. Such solutions have a curvature singularity by construction, and their initial data on a Cauchy surface to the past of the singularity can be chosen to have compact support in momentum space. They can also be truncated at large radius so that they have compact support in space, while retaining self-similarity in a central region that includes the singularity. However, the Vlasov distribution function can not be bounded. As a simpler illustration of our techniques and notation we also construct the general spherically symmetric and static solution, for both massive and massless particles.