Multiple expansion of the gravitational field in the linearized Einstein theory

By using the method of adjoint operators, the complete solution to the Einstein vacuum field equations linearized about the Minkowski metric is expressed in terms of scalar potentials that satisfy the wave equation. The multipole fields are then obtained from the separable solutions of the wave equation in spherical coordinates and the amplitude of each multipole is related to the energy-momentum tensor of the sources. The gauge- invariant components of the multipole fields are written in terms of the spin-weighted spherical harmonics and the power radiated per unit solid angle by each multipole is also obtained. (Author)