Introduction to Dipole Gravity (Gravito Magnetism)

One of the typical objections to the existence of dipole gravity has been the simple argument that "there is no negative mass in gravitation". But gravity is not electromagnetism. The analogy breaks down fast because there is no apparent magnetic counter part of gravitational phenomena in gravity like in electro-magnetism.

Strangely enough the early quest from the Princeton Wheeler group in gravitation was to look for this magnetic counter part of the gravitation. There are evidences that people considered seriously a rotating donut shaped object to create gravito magnetic effect because this configuration resembles the flow of the mass current in the circular motion as the magnetic effect is created by the electrical current in electromagnetism. All these attempts didn't produce any meaningful results.

However, it is very interesting to note that the formal mathematical expression for the actual dipole gravitational moment in the weak field limit of the linearized theory is rather simple.

The mathematical expression for the gravitational dipole moment simply asks for a displacement of the center of mass of the object in consideration without saying exactly what kind.

Unfortunately, all that has been known about the displacement of an object in physics up to then is either a coordinate translation or by giving it a simple momentum.

Both are physically meaningless because they can be transformed away, in field theoretical term, ie, the phase angle is constant. Moreover, having a displacement of the center of mass of an object without any external force is an unthinkable proposition in Newtonian mechanics because matter simply won't move or jump from one position to the other without a proper cause.

The concept of the relativistic mass increase effect has been known since the theory of special relativity has been published, but the anomalous center of mass shift due to this effect was unknown until Jeong found the system of the rotating hemisphere very peculiar, although it is clear from a moment of thought experiment using a rotating hemispherical object that it does shift the center of mass without a proper cause known in Newtonian Mechanics.

A theory in physics is like a software in modern term, which means the mathematical symbols in the equation mean nothing unless we humans attach the right meaning to it. As is well known in the software science, if one puts in "garbage" data, the software will provide us with "garbage" information. The mathematical equation in physics is very cold and impersonal in that sense. It ignores our stupidity and laughs at us from behind.

This is a quest for the gravito magnetic effect, ie, the dipole gravity.

The quest started by the simple question "what is so special about a rotating hemisphere?" and when it was noticed that a hemisphere shifts its center of mass when in rotation while a rotating sphere doesn't.

What is the cause of this anomaly?



Using the fact that the potential function is a scalar quantity, one can add the potentials from the two opposite hemispheres to construct the full potential for the sphere with the consideration of the fact that their individual centers of mass are located now R/2 from the center of the sphere toward the positive and negative directions of the z axis respectively.

This slight separation(by the distance R) of the two centers of mass of the individual hemispheres within the sphere is the key to this solution because if the two centers of mass were exactly at the same location, this dipole effect would have been canceled out exactly.

The above diagram is the quadrupole gravitational potential for a rotating sphere derived from the theory of dipole gravity. The four poles are aligned along the rotation axis of the rotating spherical shell. This indicates that the rotating sphere forms a static gravitational quadrupole moment, formed by two opposing dipoles, which is not the radiating kind. The total gravity potential(monopole plus dipole) corresponding to the diagram in an analytic form is expressed by,



The two deep potential wells (front and back) indicate the existence of two attractive dipole gravity force centers and also the repulsive ones(represented by the two tall towers ). Particles coming into the attractive dipole potential well along the rotation axis suddenly feels the giant wall of the repulsive potential and they are repelled back to the outside of the ultra compact rotating star, forming two way jet streams of the rotating black holes. It can be noticed that there is a saddle point in between the two repulsive pole towers.

A metallic ball placed at the top of the saddle point will roll down either one side or the other depending on the initial condition in a manner of harmonically increasing velocity. This is the same force that Lens-Thirring found in 1918. They concluded that this force is the evidence of the proof of Mach's principle by general relativity because of its similar nature of behaving like centrifugal force(r^2 dependence). The force toward the side of the saddle looks certainly like a centrifugal force since it depends on the square of the distance from the axis. That's why Thirring called it "Induced Centrifugal Force" in his paper. Bass and Pirani suspected the interpretation since it can be made to disappear formally by reducing the mass density of the shell of the amount increased by the special relativistic effect. They argued that this should not if the force were truly the centrifugal force.

Their fatal mistake was in the fact that they regarded the dynamic mass
increase as being the same as the permanent mass density increase. Later, Cohen speculated intuitively that this force must be due to the quadrupole effect (note the bulging effect of the sphere toward the side) which was a very close observation. Thirring also had the force in the axial direction, which is basically the harmonic oscillator as you can read off from the above graph. Now as we can see these forces are all due to the dipole effect superposed inside a rotating spherical mass shell and the cause for the jets.

As it turns out, Lens-Thirring force is a small local feature out of the many diverse features of dipole gravity ranging from zero to infinite distances and the full angular variations.

The potential also shows the dips around the equatorial plane, meaning that there is non zero contribution of dipole gravity force around the equatorial plane of the rotating stars. It also indicates that satellites tend to align to the equatorial plane because of the angular dependencies of dipole gravity.

It will be interesting to see if this potential will be able to account for most of the dark matter problems or will there still be missing matter problem even after this inclusion in the numerical computation and the curve fitting study.

In a recently published paper(2007), jets have been observed from a rotating neutron star. So, the black hole and the generally assumed associated complex mechanism must not be the absolute requirement for jets to form in the rotating ultra compact stellar objects.

Any ultra compact stellar object with high speed of angular momentum is capable of generating jets on its axis according to the theory of gravito magnetism(dipole gravity).

Note: The diagram has been fixed to make the potential to match with Lens-Thirring force. It is noted that the repulsive nature of the radial component of the dipole gravity force in the diagram is not consistent with the dark matter problem. This issue is discussed in detail in the "Sign Error in Lens-Thirring Force?" page.