Speaker: Jaydeep Singh (Princeton)

Title: Regimes of stability for self-similar naked singularities

Abstract:

A central problem in general relativity concerns the formation of naked singularities, a class of finite-time blowup solutions to Einstein-matter systems with starkly different properties than their black hole counterparts. In this talk we introduce the family of k-self-similar naked singularities, first constructed rigorously by Christodoulou, which are known to exhibit a blue-shift instability. In our main results, we quantify the strength of this blue-shift instability as the degree of concentration and the support of initial data are varied, identifying surprising regimes in which these spacetimes transition between stability and instability. We then discuss the consequences of these results for the weak cosmic censorship conjecture.