Abstract:

In his celebrated proof of the weak cosmic censorship conjecture for the spherically symmetric Einstein-scalar field system, Christodoulou exploited the following property of that specific matter model: Naked singularities, when they arise, exhibit infinite blue-shift along the null geodesics terminating at the singularity. This behaviour is consistent with self-similarity: Even for more general spherically symmetric matter models, it can be shown that self-similar naked singularities must exhibit infinite blue-shift. Whether, for these more general models, all naked singularities have the infinite blue shift property (and hence are potentially subject to an instability mechanism analogous to that introduced by Christodoulou) still remains an open question.

In this talk, we will present the construction of a spherically symmetric solution to the Einstein-massless Vlasov system which contains a locally naked singularity with finite total blue-shift along its past null cone. The initial data giving rise to this solution have limited differentiability, but belong to a regularity class above the scale invariant threshold.