University of Toronto
In the process of gravitational collapse, singularities may form, which are either covered by trapped surfaces (black holes) or visible to faraway observers (naked singularities). In this talk, with three different approaches coming from hyperbolic PDE, quasilinear elliptic PDE and dynamical system, I will present results on four physical questions: i) Can “black holes” form dynamically in the vacuum? ii) To form a “black hole”, what is the least size of initial data? iii) Can we find the boundary of a “black hole” region? Can we show that a “black hole region” is emerging from a point? iv) For Einstein vacuum equations, could singularities other than black hole type form in gravitational collapse?
Black holes have taught us that our world is a hologram --an idea precisely articulated by the famous AdS/CFT correspondence. How does the geometry of spacetime emerge from its lower dimensional dual description?
I will build a set of diffeomorphism invariant operators in 3d Anti-de Sitter space via integrals of fields over geodesics and derive their holographic duals. The latter are special CFT operators associated with a boundary subregion, called OPE blocks. I will then demonstrate that as we move the subregion, the OPE blocks undergo a local frame rotation, analogous to a Berry rotation, and the total "Berry phase" acquired over closed paths computes the length of bulk curves.