Occam's Razor

It may be refreshing to review at this point the medieval philosopher William of Occam's insight.

"One should not increase, beyond what is necessary, the number of entities required to explain anything"

Occam's razor is a logical principle attributed to the medieval philosopher William of Occam (or Ockham). The principle states that one should not make more assumptions than the minimum needed. This principle is often called the principle of parsimony. It underlies all scientific modelling and theory building. It admonishes us to choose from a set of otherwise equivalent models of a given phenomenon the simplest one. In any given model, Occam's razor helps us to "shave off" those concepts, variables or constructs that are not really needed to explain the phenomenon. By doing that, developing the model will become much easier, and there is less chance of introducing inconsistencies, ambiguities and redundancies.
Though the principle may seem rather trivial, it is essential for model building because of what is known as the "under determination of theories by data". For a given set of observations or data, there is always an infinite number of possible models explaining those same data. This is because a model normally represents an infinite number of possible cases, of which the observed cases are only a finite subset. The non-observed cases are inferred by postulating general rules covering both actual and potential observations.
For example, through two data points in a diagram you can always draw a straight line, and induce that all further observations will lie on that line. However, you could also draw an infinite variety of the most complicated curves passing through those same two points, and these curves would fit the empirical data just as well. Only Occam's razor would in this case guide you in choosing the "straight" (i.e. linear) relation as best candidate model. A similar reasoning can be made for n data points lying in any kind of distribution.
Occam's razor is especially important for universal models such as the ones developed in General Systems Theory, mathematics or philosophy, because there the subject domain is of an unlimited complexity. If one starts with too complicated foundations for a theory that potentially encompasses the universe, the chances of getting any manageable model are very slim indeed. Moreover, the principle is sometimes the only remaining guideline when entering domains of such a high level of abstraction that no concrete tests or observations can decide between rival models. In mathematical modelling of systems, the principle can be made more concrete in the form of the principle of uncertainty maximization: from your data, induce that model which minimizes the number of additional assumptions.
This principle is part of epistemology, and can be motivated by the requirement of maximal simplicity of cognitive models. However, its significance might be extended to metaphysics if it is interpreted as saying that simpler models are more likely to be correct than complex ones, in other words, that "nature" prefers simplicity.

It will be awfully redundant at this point to reiterate that the theory of dipole gravity doesn't have any assumptions other than the ones general relativity is based on itself. With such a minimal number of assumptions, the number of areas of cosmological problems it touches and provides answers are truly remarkable. The only way it can be wrong is if and only if general relativity is wrong. This perspective gives us the compelling reason to test the predictions of dipole gravity in the terrestrial experiment as soon as possible.
http://dipoleantigravity.blogspot.com/2007/04/alternative-method-of-detecting-dipole.html

Further Digression on the Mechanical Universe

The following discussion is not totally relevant to the gravity so it is debatable if it should be in the same blog which is devoted to dipole gravity or gravity in general, but it was decided that there is enough relevancy there that justifies its inclusion here than put it in a separate category.

The topic here is still about the tachyonic neutrinos. For the case of the gravitational phenomena, we strictly confined our focus on the kinematic elastic interaction of the tachyonic neutrinos with the baryonic matter particles. However, in this article we will be focusing on the non-kinematic interaction with tachyonic neutrinos. This interaction would not be totally kinematic in the sense that there is a weak interaction effect between the neutrinos and the electrons, muons and tauons(leptons). This is not a high energy interaction either because there are no new particles generated from it as in the case of the deep inelastic scattering interactions. It is not exactly like the billiard ball style collision since there is still finite distance that the interaction can be effective even though there maybe no direct contact between the particles involved. And also, there can be a vector effect like in the case of the electrons traveling in the magnetic field environment. So the effective cross section can be much larger than the case of the kinematic elastic collision. For example, there are speculations that neutrinos may be magnetic monopoles themselves, although not confirmed, if that is the case, the fast moving magnetic monopole will create circular electric field along their path exactly like moving electron creates the magnetic field around it. So the electrons can be affected by the fast moving neutrinos relatively long distance from their path which will make the interaction cross section very large. When there are so many of the fast moving tachyonic neutrinos, the space will be like a bubble bath of electric field popping in and out of them barely managed to cancel each other in the space to avoid the creation of the net electric field in the local space time by virtue of their homogeneous presence and the total isotropicity of their motion.

The situation we are going to imagine in this picture is a single hydrogen atom bombarded by the etheric tachyonic neutrinos. The proton will largely be able to maintain its position because of its larger mass compared to the electron although still its precise position will not be absolutely determined depending on the strength of the cross sections involved. However, the position of the electron will be very uncertain. If the tachyonic neutrinos have enough energy, number density and the strong enough cross section, they will collectively be able to manage to disturb the electron's position frequently and strongly enough to it make it separated from the proton to maintain the Bohr radius. Despite the extremely small physical size of the electrons, the stronger weak interaction coefficient compared to that of the kinematic interaction will be enough to make the electron afloat from the proton by the amount of Bohr radius in the ground state. So, if this is the case, the Planck constant h becomes the function of the number density, the mean velocity and the weak interaction cross section between the tachyonic neutrinos and the elementary particles.

The uncertainty principle in quantum mechanics is caused by this statistical nature of the background tachyonic neutrinos interacting with the elementary particles. For example, quantum mechanics predicts that a particle placed in the space with the initial velocity V=0 at the origin of the coordinate x=0 has less and less chance to be found at the same place as time goes by. This is a clear violation of Newtonian mechanics. It only means that there must be some particles causing this uncertainty to the elementary particles without disturbing the statistical overall average momentum and the position of the particle. This shows the key properties of the background particles, ie, their flux must be isotropic and homogeneous. So, even if the statistical effect is fully applied, the overall averaged initial location and the momentum should be the same. The question where the electron is after a while at the time t=to has no meaning in quantum mechanics. We simply don't know. The most probable location where the electron will be found is still at x=0 but the probability to find it there will be spread out so thinly throughout the space that it would become meaningless to ask where the electron is exactly located at. In the space where tachyonic neutrinos are prevalent, this is exactly what will happen to the elementary particles like electrons.

Now we see how the two phenomena, gravitation and quantum mechanics, seemingly unrelated to each other have the same origin. All the predictions of quantum mechanics will be valid, only difference is that we know now it's an excellent phenomenology because while it worked and predicted the nature so well, still it didn't provide the clear answer to the mechanically inquisitive human mind. As Einstein put it "God doesn't play dice game". We humans want to know in mechanical terms why it is working if something really works and what is behind it. "Trust me it worked million times in the past and it should work in the future, so no more questions to the validity of it" would not be enough.

So, there is a possibility that inside the stars where the tachyonic neutrinos can not penetrate with enough numbers, the Bohr radius of the hydrogen atoms could be much smaller than it would be in the open space (assuming that they(hydrogen atoms) could manage to stay as individual atoms inside the stars) because there will be much less frequency of the tachyonic neutrinos disturbing the electron's position to make it stay far enough distance from the proton to maintain the same Bohr radius as they were in the open space. Since light cannot penetrate the bulk object, it will be hard to tell if the light that we detect belongs to the quanta that generated from the core of the stars. Most of the visible light we observe will be coming from the surface of the stars. So the observation of those lights will not provide the clear answer to this question.

Another interesting question would be what would happen if all the tachyonic neutrinos simply disappear. All the matters and stars will collapse to become like tiny pieces of dots in the universe and the energy generated from it will be so large that the big bang would be an insignificant event compared to it. On the other hand, there will be no gravity so the universe will become like a soup of murky cloud, dark, dull and lifeless and meaningless presence of emptiness all over the space if there is such a thing that can be called "space" left anymore.

In fact, the meaning of the space itself would become vague and uncertain because the pressure of the tachyonic gas seems to define the space itself as we observe it, as much as the pressurized air molecules inside the balloon defines the space of the balloon itself. In fact, it can be seen that the tachyonic neutrinos are the main building blocks of the universe instead of the material particles we observe and live in them. In a sense, the material particles(stars, galaxies, etc etc) are like the sea sponges floating under the deep sea water of the tachyonic neutrino gases spread through out the universe.

Digression on the Cause of Gravity

It may be interesting to speculate at this point what may be causing this phenomenon of gravity. We are certainly in a better position than before when we had only one Newtonian gravity to find out the cause of it behind all these cosmological phenomena because the two examples will tell something about the nature of it much clearer like a detective trying to figure out a case with the same finger printings on two different incidents for the case under investigation would have much better chance to solve it.

The nature of the dipole gravity force is peculiar in the sense that it critically depends on the bulk geometrical shape of the object. This aspect was not clear from the example of Newtonian gravity since the monopole gravity is not sensitive to the geometrical shape of the object at all. Also all the elementary particles are assumed to have the same geometrical shape like a sphere.
This peculiar aspect of dipole gravity makes one wonder if quantisation of gravity is the right way to understand gravity because gravity looks like more of a bulk phenomenon than the quantum phenomenon.

So, the findings that the rotational motion creates the longitudinally asymmetric gravitational field around the rotating object like a hemisphere, cone etc may provide some additional clues.

In effect, the asymmetrical rotor must be acting like a propeller, but in what way?

Let's assume for the sake of argument that the universe is filled with tachyonic neutrinos. I published the paper titled "Neutrinos must be Tachyons" in the llnl archive which has a very good empirical evidence that it must be the case (http://www.tachyonics.com/neutrino.pdf). One should read it to see how strong the case is for it. It must be realized that there are as many neutrinos as the number of electrons and protons in the universe because the weak decay produces one in each and every cases of its interactions.

What people have not been asking is "where have those astronomical number of the neutrinos gone?" There are too many of them and the elementary particles don't simply disappear, yet, no one seems to be bothered by their apparent absence from our daily perspective of the universe.

If they are not tachyonic, they must be hanging around some part of the universe gravitating to form some kind of observable macroscopic object, which has never been found. If neutrinos are tachyonic, the case for which is very strong at the moment, they must be traveling inside of our universe incessantly. So, it is quite probable that the universe is filled with tachyonic gas like the atomic molecular gas filled up inside a balloon which may be composed of many different kinds of neutrinos if not one. After all, these tachyonic gas may form the aether itself that the light uses it as a medium to propagate like the sound wave propagates through the pressurized air filled earth surface. When Michelson and Morley performed their experiments, their major assumption was to find the solid or materialistic form of the aether not like the superluminal kind we are talking about. The aether drag effect Michelson and Morley expected to find will not exist if the aether was formed by superluminal object like tachyonic neutrinos. Furthermore, to reinforce this proposition, neutrinos are not totally immune from the light particles since they are related to each other by the electro-weak interactions. Photons and neutrinos are family members within the framework of electro-weak theory. So like in the case of the sound wave propagating through the air molecules, the compression and the relaxation of the local density of the tachyonic neutrinos generates the ripple effect to carry the light through the long distances.

The neutrinos rarely if ever interact with matters. At least that's what has been understood regarding neutrinos. However, this statement may not be entirely correct. Most of the metals and rocks are free to pass for neutrinos. However, there can be substantial kinematic non zero cross sections with baryonic matters when they are densely populated inside to form a star. The purely kinematic interaction like elastic head on collision will not produce the high energy producing strong interaction effect. So, there is really no way of knowing how the low energy neutrinos are interacting with ordinary matters. But such an elastic interaction can be expected to exist and it could be much more frequent and common than one would expect. It's basically like two billiard balls of different size collide and then bounce off from each other. The total energy and the momentum is conserved in this process, ie, the sum of the initial momentum and the energy must be the same as the final sum of the momentum and energy. Besides most of the neutrinos do not have high energy to begin with. The energy equation dictates that the lesser energy the tachyonic particle has, the faster they travel while still satisfying the Lorentz invariance. They behave in a totally different manner compared to the usual matter particles. They are not observable beside the fact that they interact kinematically with baryonic matter inside the dense stars or by the high energy neutrinos generated from the super nova interacting with the baryonic matter in the laboratory experiment.

Therefore, in a way, the core of the dense star forms a "aether vacuum" meaning that there is less and less chance for the tachyonic neutrinos can penetrate into the core of the dense stars. The strength of the aether vacuum depends on the elastic collision cross section and the number density of the tachyonic neutrinos and the average speed of them which will determine the mean relaxation time and also the characteristics of the dense object itself which will be the measure of its own density and also its volume.

So, the gravitational constant G becomes a function of those three physical quantities, ie, the number density, the average speed and the elastic collision cross section of the tachyonic aether particles with the matter.

So, here is the fundamental proposition,

The gravity is caused by the "Tachyonic Neutrino's Aether Vacuum".

Now let's see if this proposition can be consistent with dipole gravity. The rotation of the longitudinally asymmetric object creates asymmetric ether vacuum along the rotation axis, because the larger diameter side has more chance to knock off the tachyonic neutrinos due to its faster tangential velocity thereby creating the higher ether vacuum state compared to the other side where the tip of the dome or the pointed edge of the cone is located while in rotation. So there is a gradient of tachyonic vacuum pressure formed along the longitudinal direction of the asymmetric rotating object.

The lower pressure side is where matters tend to move toward and it becomes the center of gravitation. It is basically the same concept like the air plane propeller except that the tachyonic aether can not be pushed or moved by the blade of the propeller but only by the fast rotating motion of the dense object (until one can find the alternatives which will become the core of the engineering the tachyonic aether in the future).

This is also consistent with the fact that the rotating cylinder does not create dipole gravity.

The inertial effect is caused by the tachyonic neutrino's balancing act to position the object in place from all directions while trying to give it a net momentum. Of course the centrifugal force is a natural consequence of this inertial tendency of the matter in the universe. It doesn't have to require the existence of all the matters in the universe at least in a direct way. However in the process of the creation of all the matters in the universe, there must have been the same number of neutrinos generated as the number of protons in the universe which have become the part of the aether. So, there is certainly a remote relation but not in such a direct way as Mach described.

It also indicates that the empty space is pretty well balanced which means the universe is homogeneous and isotropic in terms of tachyonic neutrino's population and its density. And their fast balancing act is not hard to understand considering their immense speed of travel in the universe.

The Gaussian flux concept of the gravity force line is also consistent with this concept of the tachyonic aether vacuum because of the isotropic presence of the tachyonic neutrinos and their motions. The fundamental law of kinetic theory of gas is that the nature abhors vacuum. It must be filled up and equalize the pressure all over the space and that is also the fundamental reason for all kinds of weather phenomenon on earth.

So, in a sense, cosmology is a weather phenomenon caused by the movement of the tachyonic neutrino gas in the universe. The fast rotating black hole pushes and pulls the tachyonic gas and it produces the jets because of the imbalance and the peculiar formation of the tachyonic gas pressure in the surrounding area of the rotating galactic centers.

It's like each particles are the actors in the theater of the immense universe. They act in such a way their characters are assigned like in the Shakespearean play. Tachyonic particles have to play their role as much as baryonic matter particles play their roles.

The reason for the unusual weakness of the gravitational interaction compared to other interactions may be attributed to the fact that the kinematic elastic collision cross section of the tachyonic neutrinos with the matter particles is extremely small compared to other interactions.

The Cause of the Flat Rotational Velocity Curves

The fundamental mystery in the dark matter problem is in the flat rotation curve as the distance becomes large from the galactic center.



{courtesy from Dr. Greg Bothun}

Within the framework of the usual dark matter halo hypothesis, if the density of the halo is assumed to be constant, it will not generate the logarithmic potential which is necessary to address the flat rotation curve. If one wants to make up an arbitrary density function to make it fit the rotation curve, one has to explain how the distribution has come about that way. However, if the dark matter halo is made of the continuous cycling flux of the matter ejected by the jets, as predicted by the theory of dipole gravity, the volume density of the dark matter halo will not be constant, instead the flux density will be a constant, because it has the definite source located at the center of the rotating galaxy. The effective gravity potential produced by the dark matter halo can be expressed by



in general form, where ρ(r) represents the density function of the dark matter halo. Since the source of the dark matter halo is coming directly from the jets from the rotating galactic center, the total mass of the matter particles populated within the volume defined by 4 π r^2 times the unit length of r will be the same until the density of the halo diminishes to zero. So, the effective gravity potential within the applicable regime becomes



where M is the sum of the total mass within the volume element 4 π r^2 times the unit length of r. The logarithmic gravitational potential is the typical signature for the flat rotation curve.

The gravitational force within the relatively short distance from the center of the rotating galaxy is dominated by the strong dipole gravity force



as derived previously, which explains the sharply increasing slope in the rotation curve near the galactic center.

In his prophetic statement, Dr. Greg Bothun writes, quote

"However, it's important to realize that the "dark matter" problem exists only in the context of one known long range force (gravity). Suppose there is another long range force that we are ignorant of. If this is discovered by future physicists then they will look back at this "dark matter" cosmology much the same way we now view the early "geocentric" cosmologies."

How Lense-Thirring force is derived from dipole gravity?

Einstein's Triumphant Legacy

Although Einstein didn't live long enough to see the key solution to his own theory of gravity, dipole gravity is certainly a result of special relativity and the equivalence principle which are the fundamental building blocks of general relativity. The equivalence principle predicts that when there is an acceleration of mass, it must generate gravitational effect associated with it. And the object in rotational motion in mechanics is basically in a state of continuous acceleration in the sense that the motion requires the continuous change of the directions of the mass element within the rotating body.

But it was not clear in regard to how that works, in what way and through what kind of mechanism to cause a realistic gravitational field.

The analogy with electro-magnetism certainly failed. Rotating donut shaped object didn't create gravito magnet. Lens-Thirring's force from the rotating spherical shell indicated there is a remnant of the acceleration of the mass induced force near the center of the sphere but the interpretation and the sign of the force were incorrect. The radial component of the force was interpreted as the centrifugal force in accordance with Mach's principle and there was no explanation for the harmonic force along the axis of the rotation. And none of these forces seemed to give any clues to the existing cosmological problems. And it didn't encourage any further investigation into the subject largely because of the horrendous difficulties in analytically calculating all the details of the gravity effect from the circular motion of the spherical object. And the dipole term from the linearized theory was simply interpreted as meaningless and it was declared that there is no such thing as dipole gravitational moment as a physically meaningful entity.

Thus, the question remained a fundamental mystery of general relativity. How the circular motion of the mass manifests itself into a verifiable gravito magnetism?

Even if the rotating frequency and the tangential velocity of the object may be considered crucial to the effect, it was not obvious how it should be incorporated into the final form of the gravito magnetism. The most crucial and final stumbling block may have been Newtonian mechanics itself since there is no such thing as the shift of the center of mass by a fixed definite quantity depending on the speed of the rotational motion in Newtonian mechanics. It simply won't happen. Of course, this can be used to perfectly justify the claim of the non existence of the gravitational dipole moment if and only if one assumes that Newtonian mechanics is the flawless and complete theory of the mechanical universe.

Dipole gravity(gravito magnetism) is a plain and inevitable solution to general relativity that has been sought but eluded the researchers in the field for a long time. Clearly it was not obvious to Einstein himself. But there is no doubt that it is still one of his most triumphant legacies.

He would have been very happy to see the solution of his own theory explaining the mysteries of the universe ranging from the jet phenomena to the dark matter problems which did not emerge as the prominent cosmological problems at his time.

We can learn here the pattern regarding on how the old and new principles of physics exchange and compete to evolve into a new principle to teach us something new. When there is a new principle which is larger and incorporating the old principle, there is a crucial and unique mechanism that shows the clear conflict between the old and new principle at which point one is forced to choose one and thereby face the demands of the modification of the old principle to make it compatible to the new one.

In any circumstances, the final result is that it forces us to abandon certain features of the old principle. This happens in a continuous fashion in the history of mankind and that is how the secret of the nature is continuously made comprehensible.

What is at Stake?

If special relativity is correct as it has been proven to be over the times, dipole gravity is one of the inevitable consequences of its many different aftermaths.

Dipole gravity can not be avoided once special relativity becomes the major frame work of the space time fabric via Lorentz transformation . Because the center of mass of a rotating hemisphere pauses a great dilemma if Newtonian mechanics is considered to be the absolute law of physics at the same time with special relativity.

We can not take both to be absolutely correct when they are contradicting each other in such a glaring fashion.

Should we choose Newtonian mechanics over special relativity and discard the predictions of dipole gravity altogether?

I don't think this possibility will ever occur in the minds of any physicists today.

The alternative may be then "Are we ready to take the bold step to embrace dipole gravity and compromise the old principle of Newtonian mechanics in accordance with the newly discovered principle of dipole gravity?". The voluntary motion of the gravitational dipole moment predicted by dipole gravity is certainly not consistent with Newtonian mechanics let alone the jets from the black hole accretions discs. It must be realized that there is a serious paradigm gap between the observed universe and the presently known tools of physics.

The reason for this question is because that is exactly what we are facing at the moment with the mounting problems of cosmology if we truly want to begin to comprehend the vast mysteries of the universe.

Black Hole Jet Engine (Relativistic Jets)

The intricate structure of the jet engine can be studied from the three dimensional picture in association with the Z directional dipole gravity potential at the center of the star. The compressive and also attractive quadrupole gravity force has the effect of collecting the dark matters scattered around the rotating star toward the equatorial plane.

This same force squeezes the matters and feeds them into the central location of the black hole engine because that's where all the quadrupole gravity force lines are merging into. Please note that if Lens-Thrring's force (that is the out going force from the center) had been correct, this compressing force would not have been possible. Now the Z directional potential indicates that the matters accumulated at the center of the engine are pushed away from the dead center toward the direction of the both sides of the poles as the central Z directional potential below indicates the down hill slope toward the center of the each of the hemispheres.

As the more and more matters are accumulated on these shallow potential dips with the extremely hot temperature because of the enormous pressure due to the continuous feeding mechanism of the dipole gravity force, some of those hot matters will be pushed over toward the edge of the hills of the repulsive potential on both side of the poles.

Once the matters cross over the repulsive potential hill, they will be pushed out of the poles like rolling down the steepest downhill that has ever existed in nature. The rapid expansion of the volume will make them cool down very quickly while still under the enormous repulsive force from the poles of the star until the monopole gravity takes over and starts to bring them back especially the ones went straight line following the axis. In this process, some of those coming back will collide with the ones came out of the poles at later times to generate the enormous visible radiation.

The ones went off the lines of the axis will be pulled back by both the monopole and the dipole gravity force toward the center and also toward the equatorial plane to recycle the whole process again.

These matters on transit for the recycling constitutes the dark matter halo around the surrounding space of the active galactic nuclei. The reason they are not visible is because they are in constant motion following the dipole gravity force lines. The lobes at the end of the jets can be explained as due to the stationary state of those particles because it gives them enough time for the condensation and gravitation as well as the nucleosynthesis. At the end of each of the jets, the ejected particles are in a complete balance between the repulsive gravity force of the dipole and the attractive monopole gravity force and they virtually stop their motion. It must be noted that the two mechanisms that make the cosmic matter visible from the hundreds of millions of light years away are either by the massive collisions among themselves or by the mutual gravitation and the subsequent nucleosynthesis. If those matters are constantly traveling and spreading out in space, there is no way they can be visible.

It must also be noted that this intricate black hole jet engine mechanism does not require any other assumptions than the quadrupole gravito magnetic effect from the rotating star itself. The jet mechanism starts from the first principle of the dipole gravity force. The extremely hot temperature and the corresponding high pressure of the hot matters inside the galactic center are not the enough conditions to allow them to be ejected from the black hole. Without the strong repulsive gravitational force from the quadrupole gravito magnetism, light itself will be trapped and there is no chance for the high pressured hot matter to escape the event horizon.

So, it is puzzling how anyone can explain the jet phenomenon without invoking the repulsive gravity effect without contradicting him/herself. Because once the event horizon is defined as the line that can not be crossed even by the light, there is no escaping for any matter with any pressure or temperature regardless of whether they are in plasma state or under intense magnetic field to have any chance to escape from it.

How Gravito Magnetism is Different from Electro Magnetism

Electromagnets can be created by electric current flowing through the magnetic wire wound around a metallic cylinder. The direction of the current determines the polarity of the magnets. So the direction of the movement of the charge is crucial to the determination of the polar properties of the magnetic force.

On the other hand, in the gravito magnet case, the direction of the rotation is not a factor in determining the polarity of the poles. So the similarity stops here quickly.

The following statement provides us with the current insight into the gravitomagnetism. "Gravitomagnetism is produced by stars and planets when they spin. "It's similar in form to the magnetic field produced by a spinning ball of charge," explains physicist Clifford Will of Washington University (St. Louis). Replace charge with mass, and magnetism becomes gravitomagnetism" quoted from http://science.nasa.gov/headlines/y2004/19apr_gravitomagnetism.htm.

However, there is no observed gravitational phenomenon that indicates the dipole gravito magnetic effect from a rotating spherical object as a whole. Because if that is the case, we will observe the weaker gravity force in the north pole in comparison to that of the south pole or vice versa, which has never been observed. And also the jets from the black holes would have to be only from one pole not from the both poles as observed.

The asymmetricity of the object along the rotation axis determines the polarity of the gravito magnet. For example, a cone, a hemisphere, etc will produce a gravito magnet in rotation but a rotating cylinder will not. (This point has been discussed by Bass and Pirani previoulsy where they objected that Lens-Thirring force can not be the centrifugal force because a rotating cylinder also must have a non zero Lens-Thirring force, but it doesn't. However, one can always argue that the Universe is not a cylindrical shape.)

The wider area becomes the attractive pole and the sharp and narrower area determines the repulsive pole regardless of the direction of the rotation around its symmetry axis.

The reason a spherical rotor can create a quadrupole gravito magnet is because the asymmetricity of it changes at the equatorial plane ie the radius in relative to the rotation axis increases along the Z axis and then at the equatorial plane it starts to decrease, which means that it is an oppositely stacked two dipole gravito magnets. Thus, a rotating spherical object becomes a quadrupole gravito magnet in which the equatorial plane becomes the region where the attractive gravito magnetic poles are faced to each other.

The gravito magnetic force lines come out of the both poles and merge into the equatorial plane and then joined together to come back into the center and then go back out of the both poles.

Probably 99 percent of the rotating stellar objects, if not all, including the black holes in the universe may be described as a quadrupole gravito magnet in addition to the typical gravitational monopole. When the monopole gravity dominates the gravitational interaction, the shape of the object will most likely tend to become spherical. However, as the rotational motion starts to kick in, the general shape of the star will be more like an oblate sphere or a superposed saucer shaped disk which will in turn accentuate the gravito magnetic effect and accelerate the process of becoming a black hole with enormous jets.