Causal Structure at Infinity and the Positive Mass Theorem

27.10.2022, 14:00-15:30  –  2.22 und Zoom
Geometric Analysis, Differential Geometry and Relativity

Peter Cameron

A spacetime is said to satisfy the Penrose property if every pair of points on past and future null infinity can be connected by a timelike curve. Penrose showed that this property fails in Minkowski spacetime of any dimension but is satisfied in 3+1 dimensional positive mass Schwarzschild. I will consider the Penrose property in more detail and discuss how it is related to the ADM mass and dimensionality of the spacetime. I will then show how some of the ideas arising in the study of this property can be used to prove a version of the positive mass theorem. Finally, I will discuss how the apparent failure of the Penrose property in higher dimensions (regardless of the ADM mass) may be linked to the greater regularity of possible conformal completions of the spacetime at spacelike infinity.

This talk is part of the seminar Geometric Analysis, Differential Geometry and Relativity organized by Carla Cederbaum (Uni Tübingen), Melanie Graf (Uni Tübingen), and Jan Metzger (Uni Potsdam) . To obtain the Zoom data please contact jan.metzger@uni-potsdam.de