POST-NEWTONIAN GENERATION OF GRAVITATIONAL-WAVES .2. THE SPIN MOMENTS

This paper extends the multipolar gravitational wave generation formalism of Blanchet and Damour [6] by deriving post-Newtonian-accurate expressions for the spin multipole moments. Both the algorithmic and the radiative spin multipole moments are expressed as well-defined compact-support integrals involving only the components of the stress-energy tensor of the material source. This result is obtained by combining three tools: (i) a multipolar post-Minkowskian algorithm for the external field, (ii) the results of a direct multipole analysis of linearized gravitational fields by means of irreducible cartesian tensors, and (iii) a study of various kernels appropriate for solving the quadratic nonlinearities of Einstein's field equations.