Guests

Riemannian Penrose inequality gives the upper bound of the area of the outermost minimal surface in an asymptotically flat space with nonnegative curvature. This inequality shows, roughly speaking, the upper-bound area of black hole horizon, that is, it can be applied in a region with a strong gravitational field. We generalize this inequality so that it can be applied in weak gravitational fields, hence a generalization of Riemannian Penrose inequality.

This mini course (consisting of six talks) will introduce the basic techniques of optimal transportation in smooth Lorentzian geometry. Starting from the existence of causal couplings and optimal causal couplings, we will discuss dynamical optimal couplings and their structure (i.e. the Mather graph Theorem). Further topics include the Monge problem in Lorentzian geometry and Kantorovich duality. Conditions for the existence of dual solutions will be discussed as well. The last part of the course will be devoted to the characterization of the Einstein field equations via optimal transportation.

Kerr spacetimes are solutions of vacuum Einstein field equations and model the gravitational field around rotating black holes. The natural analytic extension of the Kerr spacetime over the horizons and in the negative radial region, called Kerr star, contains closed causal curves. Despite causality violations, I will sketch the proof of the nonexistence of closed null geodesics in the Kerr-star spacetime.