Debye potentials for the gravitational field

Abstract

Debye potentials for the gravitational field of a bounded system are given. The field equations of the linearized theory of gravitation are written in a form very similar to Maxwell's equations using field strengths which are the components of the Weyl tensor. The Debye potentials are then closely related to the two non-transverse components E RR and B RR . These components completely determine the field in empty space and give a simple characterization of the field in terms of two scalar quantities. In order to express the remaining field strengths simply in terms of the Debye potentials, a toroidal and poloidal representation of symmetric, traceless, divergenceless, 3-dimensional tensor fields is developed. The spherical components of these tensor fields are given in terms of spin-harmonics. The Debye potentials' explicit dependence on the sources is given in terms of a multipole expansion and the general expression for the momentum loss of a bounded system due to gravitational radiation is calculated in terms of the multipole moments. The properties of the field in the near and far field zones are discussed.