New York General Relativity Seminar, 2014

Speaker: Lydia Bieri

Title: “Analysis of Radiation for the Einstein and the Maxwell Equations”

Abstract: A major goal in the study of Einstein’s equations is to investigate the analytic properties and geometries of the solution spacetimes. In particular, fluctuations of the curvature of the spacetime, known as gravitational waves, have been a highly active research topic, as we are believed to be on the verge of their detection. Understanding gravitational radiation is tightly interwoven with the study of the Cauchy problem in general relativity (GR). Gravitational waves leave a footprint in the spacetime regions they pass, changing the manifold permanently. This is known as the Christodoulou memory effect. It has been believed that for the Einstein equations, being nonlinear, there exists one such effect with a small `linear’ and a large `nonlinear’ part. In this talk, I present some of my recent work with D. Garfinkle showing that these are in fact two different effects. We will also consider the case of the Einstein-null-fluid equations describing neutrino radiation as present in events like core-collapse supernovae. Moreover, we establish two analogous effects for the (linear) Maxwell equations as well as for a nonlinear electromagnetic theory.

Speaker: Xinliang An (Rutgers University)

Title: “Formation of Trapped Surfaces in General Relativity”

Abstract: In this talk, I will present two results regarding the formation of trapped surfaces in general relativity. The first is a simplified approach to Christodoulou’s monumental result which showed that trapped surfaces can form dynamically by the focusing of gravitational radiation from past null infinity. We extend the methods of Klainerman-Rodnianski, who gave a simplified proof of this result in a finite region. The second result extends the theorem of Christodoulou by allowing for weaker initial data but still guaranteeing that a trapped surface forms in the causal domain. In particular, we show that a trapped surface can form dynamically from initial data which is merely large in a scale-invariant way. The second result is obtained jointly with Luk.