Gravitational radiation theory uses the multipole expansion to express the gravitational radiation from a localized slowly moving source. This expansion shows that the radiation is dominantly quadrupolar, unlike electromagnetic radiation, which is in general dipolar. The quadrupole moments are referred to in this case as the mass and current moments
More information can be found in the paper: Blanchet, L. (1998). On the multipole expansion of the gravitational field. Classical and Quantum Gravity, 15(7), 1971.