Null surface geometrodynamics

Abstract

Investigates the dynamical structure of Einstein's theory of gravity using a time parameter whose level surfaces are null hypersurfaces in spacetime. A spacelike foliation of codimension two is used in order to give an invariant kinematic description. Dynamics are analysed via a constrained Hamiltonian formalism. It is found that the Hamiltonian formulation includes both first and second class constraints. The first class constraints are associated with the invariance of the theory with respect to diffeomorphisms of the null hypersurfaces. The second class constraints are direct consequences of the choice of null time parameter.