Symmetry in Nonlinear Mathematical Physics - 2009

Eyo Ita (United States Naval Academy, Annapolis, USA & University of Cambridge, UK)

Proposed solution to the initial value constraints of general relativity in four dimensions

The initial value constraints are a currently unsolved problem in the full theory in 4D general relativity, due to the Gauss' law constraint. In this talk we provide a solution to all of the constraints by transforming GR into a new set of variables which encodes the physical degrees of freedom. The Gauss' law constraint then becomes a second-class constraint, which is directly integrable to its solution. We express the physical states of GR in terms of the algebraic classification of the spacetime, in conjuction with a nonlinear transformation into the Lorentz frame solving the Gauss' law constraint. The final result is our proposal for the general solution to the initial value constraints problem by explicit construction.