Hamiltonian technique for the construction of asymptotically flat metrics. I. Stationary axisymmetric gravitational field

Abstract

As a first step towards the investigation of more general asymptotically flat metrics, a new technique is devised which, within the framework of the Hamilton formalism and using proper boundary conditions for a stationary axisymmetric gravitational field, yields the Kerr metric. This metric appears as a 'first-order correction' with respect to the Schwarzschild metric which is built into the more general metric. This goal can only be attained if one introduces so called 'kinematical momenta'. A physical interpretation of these momenta becomes possible if one studies the force exerted by the Kerr field on a spinning test particle.