Reduction to first order of the Hamiltonian Constraint of General Relativity

TL;DR

This paper introduces a method to simplify the Hamiltonian constraint in general relativity by reducing it from second to first order using orthonormal triads and a flat Weitzenbock connection, without adding extra equations.

Contribution

The work presents a novel reduction technique for the Hamiltonian constraint in general relativity, simplifying its order without increasing the number of equations.

Findings

Hamiltonian constraint reduced to first order

Method uses orthonormal triads and flat Weitzenbock connection

No additional equations introduced by the reduction

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.