Geometry of expanding black hole cosmologies

Volker Schlue (Melbourne)

Abstract

In general relativity, the so called Schwarzschild de Sitter spacetimes are the simplest models of a black hole in an expanding universe. I will describe the geometry of these 3+1-dimensional Lorentzian manifolds, and describe progress on a related stability problem for the Einstein vacuum equations. It turns out that the conformal Weyl curvature plays a central role in understanding the evolution of expanding spacetimes, and I will discuss a phenomenon known as the global redshift effect.