Global Studies of Einstein Spacetimes

Yale University, New Haven CT

Investigators

Abstract

This award supports projects to explore fundamental issues in Einstein's general theory of relativity (GR). One project examines the evolution of spacetimes to see if the development of singularities that signal the breakdown of GR can occur in nature only inside black holes and, within black holes, can be visible only to observers who run into them. This is called the Cosmic Censorship Conjecture. This question will be addressed through continued development of light­cone­ estimates for the Einstein equations that parallel those that have already been developed for the Yang-­Mills-­Higgs equations. The objective will be to show that space­time curvature cannot blow up (point­wise) in a (vacuum) solution to Einstein's equations until the integrated (Bel­-Robinson) energy for curvature blows up. Another project will be to continue the development of improved numerical methods for the study of black hole collisions. Recent work has established the regularity of the (conformally transformed) ADM evolution equations at null infinity. This result and its potential generalizations will be applied to actual numerical calculations. The cosmic censorship conjecture is often considered to be the main open mathematical problem in classical general relativity. Cosmic censorship is the natural analogue, for Einstein's equations, of the global existence property for Minkowski space field theories and so it seems very plausible that techniques that have proven successful in the analysis of the latter should have something important to contribute to the former. In addition, any significant progress on the development of improved numerical methods for the analysis of black hole collisions can be anticipated to strongly influence the ongoing worldwide efforts to numerically model these important astrophysical processes and ultimately to impact LIGO and LISA observations. Much of this research should be of interest to mathematicians. Development of improved numerical methods for the computation of gravitational waves from colliding black holes could have an impact on the experimental search for such radiation. Postdoctoral fellows and graduate students are expected to play key roles in these projects.