Principal Investigator: Lars Andersson
The principal investigator is proposing to do research on problems relevant to Lorentzian Geometry, General Relativity and Riemannian Geometry. The main focus of his research, the Cauchy problem for the Einstein equations, interacts deeply with each of these areas. Among the topics considered in this proposal are global stability of cosmological models, the theory of marginally trapped surfaces and dynamical horizons, and the structure of cosmological singularities. Andersson will attempt to prove that in the case of spacetime dimension at least eleven, there are families of vacuum cosmological models which are globally stable, with quiescent singularity. In the 3+1 dimensional case, similar results are expected to hold for the Einstein-scalar field equations. Andersson and collaborators have recently been able to apply techniques developed in the theory of minimal surfaces to the case of stable marginally trapped surfaces, which play the role of apparent horizons in general relativity. Andersson plans to pursue the connection between marginal surfaces and minimal surfaces in his future research, and to apply these techniques also to dynamical horizons. In addition to the above topics, Andersson proposes a program of research using analytic and numerical techniques, directed towards investigating the asymptotic behavior of general inhomogenous cosmologies near the singularity.
The Einstein equations describe the geometry of spacetime, which in turn determines the motion of bodies (planets, stars, galaxies) in space, as well as the dynamics of fields and particles via their respective field theories. The geometric view of the universe provided by the Einstein equations has led to some of the most fundamental and paradoxical features of our picture of the universe, including the initial spacetime singularity or Big Bang and black holes. The mathematical study of spacetimes in extreme conditions such as near the Big Bang singularity or near the singularity in black holes has led to a far reaching conjecture called ``Cosmic Censorship'', which implies that phenomena which violate the intuitive notions of causality must be hidden (censored) from observers. In this project, problems related to cosmic censorship are studied using a combination of computer based and analytical techniques, with a particular focus on the evolution of geometry from initial conditions.
