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.