The Problem of Evolution in General Relativity

Princeton University, Princeton NJ

Investigators

Abstract

PI: Sergiu Klainerman, Princeton University DMS-0245368 Abstract: The main goal of the proposal is to investigate the regularity properties of the Einstein field equations of General Relativity as well as those of other important physical systems. Most emphasis be given to the `` Bounded square integrable curvature conjecture'' according to which the initial value problem for the Einstein-vacuum equations is well posed with only square integrable bounds on the curvature of its initial data set. The PI believes that this is an essential foundational step towards a general regularity theory of the Einstein equations. By concentrating on the issue of minimal regularity assumptions for which the equations can be uniquely continued it is hoped that we can find, at least, some of the tools needed in understanding the onset of singular behavior. One of the fundamental tasks of mathematical physics is to provide a full, qualitative, description of black holes and singularities of solutions to the Einstein equations in General Relativity. The principal investigator has established a program which he hopes that will provide the rigorous mathematical foundations of such a theory. The main goal of this present proposal is to establish the minimal regularity assumptions that needs to be verified by the initial conditions such that one can still make sense of a physical solution to the Einstein field equations. The proposal also envisages research in connection to other important equations of mathematical physics such as those governing the behavior of collisionless particles in an electromagnetic field.