The radial component of the above dipole potential(second term) changes its sign from positive to negative as the latitude angle crosses over the equatorial plane where the latitude angle theta is 90 degree, which means that the gravity force from this dipole moment changes from attractive to repulsive because taking the gradient of the dipole term in the spherical coordinate system will leave the cosine factor untouched.
Do we have antigravity force in our universe?
Can this effect be tested?
I think it depends on the sensitivity of the gravitometer and the physical limitation of the speed of rotation of the giant hemispherical rotor that might be used. The material strength, the density of the material and the nano scale structural imperfection of the rotor in bad combination could result in a devastating catastrophe when the rotational speed gets to a maximum level.
However, one promising feature of this future experiment is that it is controllable.
We don't have to wait for the very precious guest not knowing when and in what dress will he/she make a visit, as it is like in LIGO experiment. Perhaps it may never make a visit and even if it does, we may accidentally miss the opportunity to see it.
All these possible predicaments are not working for LIGO.
How real is this dipole gravity potential?
If there were a super computer which can calculate all the gravity effect generated from the acceleration of each of the mass components within the rotating spherical shell, it would have come up with exactly the same potential derived from the theory of dipole gravity.
How do we know that?
Because the dipole gravity potential matches with the one calculated by analytic method used by Lens-Thirring in the region close to the center of the sphere. The analytic method is not very effective when the term contains singularities as can be seen in the dipole gravity potential. All those deep wells and the high pole towers are the regions typical analytic calculus fails.
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