A quadrupolar electrical charge distribution is equivalent to an arrangement of four electric charges, two positive and two negative. This applies to gravitational "mass charge" distributions as well. For example the Earth isn't spherical, it's an oblate spheroid, so its mass-charge distribution has a quadrupolar component, because an oblate spheroid is equivalent to a spherical charge distribution that's modulated by four gravitational mass-charge poles. This is why gravitational radiation is quadrupolar - it's only produced by a changing quadrupolar mass-charge distribution, like a binary star system undergoing major-axis rotation.
But as Robert L. Forward showed in his 1990 paper
Negative Matter Propulsion, which was based on earlier work by Hermann Bondi in 1957, an opposing pair of gravitoelectric charges will self-accelerate along their alignment axis due to the sign of the charge interactions. He illustrated the concept in its simplest Newtonian form four years before Alcubierre designed a slightly more complex solution in the tensor field language of general relativity, but they're very similar solutions in nature. Robert Forward simply focused on the mass-charges, whereas Alcubierre focused on the spacetime metric. They've both only been interesting in the sense of a theoretical toy model though, because both solutions require high densities of negative mass-charge, which is probably physically unattainable.
That's why Jack Wisdom's 2003
Swimming in Spacetime concept for a new form of gravitational field propulsion is so interesting - he showed that an oscillating quadrupole comprised only of four positive charges can climb upward within a gravitational field. In my mind the significance of Dr. Wisdom's discovery cannot be overstated because it represents the first form of gravitational field propulsion to be discovered which requires neither exotic negative mass-energy, nor extremely high magnitudes of high mass-energy.
So I think it's only a matter of time and ingenuity for the next theoretical breakthrough in the field of gravitational field propulsion, before we discover a propulsion concept which is both technologically realizable and ideally suited to achieve superluminal interstellar spaceflight, as so many of our galactic neighbors seem to have already achieved.