Principal Investigator: Lars Andersson
This proposal aims to investigate the Cauchy problem for the Einstein equations. Several aspects will be studied, including nonlinear stability of cosmological spacetimes, as well as the nonlinear stability of various versions of the Einstein equations for spacetimes with one spatial Killing field. Studies of the asymptotic behavior near spacetime singularities will be carried out, with particular attention to aspects of the BKL proposal and asymptotic silence. Here a combination of numerical and analytical methods will be used. Elliptic gauge formulations for the Einstein equations will be investigated. These are of interest for large scale numerical computations, as well as for the Cauchy problem for rough initial data.
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.
