Tom Roberts:
Bilge wrote:
What is a dipole? Draw a + and -
charge and the field lines. The dipole moment is just p = qd and points in
the direction from +q to -q. Now draw two masses. (call one your mass and
the other your "external" field, if you like). We don't have any negatives
masses, so the field can't point from one mass to the other. There are no
gravitational dipoles. The lowest order multipole moment is a quadrupole.

Consider a single pointlike mass. It is a monopole.

Consider two pointlike objects of different mass, separated by a small
distance looked at far away. The multipole expansion of this is a
monopole plus a dipole. While no pure gravitational dipole exists, it is
CERTAINLY possible for a system to have a nonzero gravitational dipole
moment.

Still, even though gravitational monopoles and dipoles exist, there is
no monopole or dipole gravitational radiation. As others have pointed out.

That's only an artifact of the coordinates you choose to write the
multipole expansion. A single point mass (or charge) trivially has
a multipole expansion m\sum r^l Y_lm(\theta, \phi). However,
for a system of masses, you can choose coordinates in which the
dipole moment vanishes, i.e., the center of mass. That isn't true
for charges and the reason is the one I gave.