How to Falsify Dipole Gravity?

There may be several ways to theoretically dispute the validity of dipole gravity.
1. There is no mass increase effect due to special relativity.
2. There is no ideal solid object in relativity theory.
3. Hemisphere may deform while in rotation so that it may cancel the shift of the relativistic center of mass.
4. Relativistic shift of the center of mass has nothing to do with the dipole gravitational moment in general relativity.
5. There may be dipole gravity effect but the spherical shape of the source will completely cancel the effect.
6. Ehrenfest paradox negates the effect of the relativistic center of mass shift.

The statement number 1 is a false. The special relativistic mass increase effect has been observed and confirmed. The statement number 2 has been discussed in the paper "Non Newtonian force...." In fact, the question of the rigidity must be considered a relative one. Depending on the binding force of the dense stellar object, the degree of rigidity will vary. The statement number 3 can be disputed by the fact that, in general, the longitudinal asymmetry is all it needs to have a shift in the center of mass of a rotating object, so the deformation itself doesn't affect the fact that it will have a shift of the center of mass. The statements number 4 and 5 can be disputed by the fact that dipole gravity reproduced the exact form of the Lense-Thirring force at the center of the rotating spherical shell.

Now regarding the statement number 6, some readers of the dipole gravity article objected to the notion that there is a relativistic center of mass shift for a rotating hemispherical rotor by invoking Ehrenfest's paradox, which states that due to the length contraction effect of special relativity, the circumference of a rotating ring will be shorter than given by 2piR(the length of the radius will still be the same).

So the mass of the rotating ring should be the same regardless of the speed of the rotation according to their objection.

However, if we assume that the ring is made up of N number of atoms connected in series, each atoms will experience the special relativistic mass increase effect, and since the number of the atoms can not change due to the rotational motion, the relativistic mass increase effect for the whole ring(as well as for the whole hemisphere) should still be effective.

The next objection is from the simple comparison with the electromagnetic phenomenon. The electricity and magnetism has electric and magnetic dipole moment because there are two different charges in the theory of electromagnetism, ie, positive and negative charges of electricity and north and south poles of magnetism, but there is no negative mass in gravity so how can you have gravitational dipole moment?

While gravity and electromagnetism are both long range forces, they are fundamentally different forces of nature. In fact, the fact that there is no observed negative mass in the universe has contributed greatly to the notion that there should be no gravitational dipole moment in the physical world. However, general relativity in the linearized form only requires a physically meaningful shift(not the kind that can be eliminated by a coordinate translation) of the center of mass, not the presence of a negative mass for the existence of a gravitational dipole moment.

The question on why this shift implicated in the linearized theory of general relativity should be identified with the relativistic shift of the center of mass of a rotating longitudinally asymmetric object may be entirely a matter of faith. There is no reason it should be identified as such. But then there is also no reason it should not. At least it confirmed the result calculated by a different method of analytic integration performed by Lense-Thirring.

As in the Dirac's equation of the relativistic theory of positrons, a mathematical equation can be interpreted by predicting a certain new physical reality.
The entire justification of such an interpretation totally remains in its predictive power of the physical nature.

So the last resort to falsify dipole gravity remains in the test of its fundamental predictions since all the features of the dipole gravity potential have been consistent with the observed cosmological data.

Newtonian gravity started from the conceptual extension of the force that was observed from a falling apple(the real story behind will be much more complicated and deeper than can be described by such a simple story), the same force is exerted in the planetary system as well as in our daily lives. It seems clear that the massive cosmological phenomena like the jets and the dark matter problems should have a similar counter part in our daily lives so that we can observe it. Since dipole gravity is the second order effect from general relativity, its strength should be much weaker than Newtonian gravity and as such its effect will be much harder to detect in the terrestrial environment. But it is certainly within our current technological reach to test it as shown in the previous pages.

What if the test disproves the prediction?

I think it is possible, but it will ultimately mean a disproof of general relativity.