Reduction to first order of the Hamiltonian Constraint of General Relativity

Abstract

In this work, a method for solving the constraints of general relativity is presented, where first all geometrical objects are written in terms of a set of orthonormal triads and a flat Weitzenbock connection, which depends on the triads and on a flat spin connection. It is shown that the hamiltonian constraint can be reduced from a second order equation to a first order one. Even though the order of the equation is reduced, we do not get any extra equations to solve by this procedure. A conformal decomposition is also presented.