Global existence problems for the Einstein equations

University Of Miami, Coral Gables FL

Investigators

Abstract

DMS-0104402 Lars Andersson This proposal is concerned with the global existence and cosmic censorship problems for the Einstein equation, and related issues in Lorentzian and Riemannian geometry. One of the primary goals is to prove a nonlinear stability result for the Einstein equation in the cosmological case. For large data, global existence is a very hard problem, and here the aim is to identify and study model problems as well as lower dimensional problems derived by symmetry reductions. The structure of cosmological singularities will be studied from the point of view of the BKL proposal. For flat, spatially compact spacetimes, global constant mean curvature foliations will be studied, in particular their asymptotic behavior in the expanding direction and near the singularity. The Einstein equation, which describes the interaction of matter with spacetime geometry, is one of the fundamental classical field equations of modern physics. According to the world view of modern physics, our universe is described on large scales by one of the simplest solutions to the Einstein equations, the Friedman-Lemaitre solution. According to this picture, the universe has developed from a singularity (big bang) and is expanding. The work in this project is concerned with the nonlinear stability of this model, the behavior of spacetime in extreme conditions near the big bang and its ultimate fate in the expanding direction.