Origin of Dark Matter Halo and the Cause of the Dark Matter Problem

It can be seen from the general dipole gravity force lines around the rotating spherical mass that the latitude angular dependent force of dipole gravity actually can force the matter around the rotating galaxy toward the equatorial plane.

This means that the matters ejected through the poles by the jet mechanism especially the ones that drift away from the rotation axis can actually come back to the equatorial plane to recycle the whole process again.

Those matters that are on the way of coming back toward the equatorial plane will not be visible because of the lack of the force that can make them stay in the same location for a long enough period of time for the condensation and the gravitation and also because of the significant reduction of the collision cross section between the incoming and outgoing particles off the course from the axis of rotation.

So there is a strong possibility that the dark matters are not only populated around the equatorial plane but also around the whole space surrounding the rotating galactic center like a halo(dark matter halo). They are there but can not be visible. There is an issue of the visibility of the dark matters when they are made of gases and dusts. However, in the jet mechanism, because of its sudden expansion of the volume when they are ejected from the port of the poles, there is a strong chance that the matters will be cooled down quickly and condensed into a much bigger size than gases or dusts.

The force lines in the gravito magnetic concept of dipole gravity makes it a lot clearer on how the matters will behave around the strongly gravitating rotating ultra compact stellar objects.
Due to the point source nature of the active galactic nuclei compared to the sheer size of the volume of the galaxy itself, matters ejected from the ports form a distribution function in such a way that the outgoing flux density is constant, which is the main cause of the flat rotational velocity curves observed in the spiral galaxies.
Of course, this density distribution function is valid only up to the point where the finite boundary of the dark matter halo ends. Naturally, it is expected that the distribution function will be a sharply decreasing function than the typical 1/r as it comes close to the boundary of the dark matter.

Derivation of Lense-Thirring force from Dipole Gravity

Is Space Travel Possible Using This Gravito Magnetic Propulsion System?

At the present level of understanding of gravito magnetism and the available technology, the answer is no.

We do not know exactly why this phenomenon is possible in the first place. It will eventually lead us to the more fundamental understanding of the nature and then we will be able to engineer it.

In all practicality, turning a wheel at the speed of 1,000,000 rpm is barely possible at the moment in the form of the ultra centrifuge. And the gravito magnetic force generated from it is minuscule. However, if one can assume that the proper technology will be available in the future, there is no theoretical limit of speed that people can travel. And also, this mechanism of propulsion does not require continuous supply of energy in principle because of the conservation of the angular momentum of the gravito magnetic dipole rotor.

It is not hard to imagine the process of a star becoming a black hole because of the final crunch of the density and its radius, even without Schwarzschild metric. It's a seamless logical conclusion except that the metric provided the fundamental ground for the mathematical details in its process. Black hole is a logical extension of Newtonian gravity plus the equivalence principle and special relativity.

Now we can perform exactly the same logical extension for the gravito magnetism. This perfectly imaginable mechanical process produces the means to travel the universe with little expenditure of energy. Could the wormhole be the logical macroscopic extension of the gravito magnetism?

In the remote future, when the true cause of the gravity phenomenon is understood in depth in relation to the electricity and magnetism, we will be able to engineer it in a much more efficient way than the brute force turning of the massive wheel.

Thoughts on Nomenclature, How Do You Name It?

After all, it can bee seen that a rotating sphere, donut shaped ring and a rotating football shaped object along the long side of axis etc. creates static gravitational quadrupole moment or two superposed gravito magnets and that it's a very general feature rather than exceptions. The core of the fast rotating galaxy may have the shape of the two superposed saucers due to its strong expansion around the equatorial plane of the rotation axis.

There was a thought about the name of this phenomenon. Basically it's a static gravitational phenomena because it is not radiating. However, in terms of the motion of the source in rotation, it resembles the mass current like in magnetism. In a way, it looks so much like a magnetic counter part of gravity.

However, this entity is originally from one of the terms in the linear expansion of the weakly gravitating object in general relativity, ie. the second order term next to Newtonian(mono pole) gravity. So, it is certainly the dipole gravity. There can hardly be any doubt about that.

The only problem with it is that, if you talk about gravitational dipole moment, it sounds like there are two different types of mass creating one, which is a nonsense, as we are so much used to the nomenclature of the electricity and magnetism.

In terms of the properties, I think there is a lot more similarities with magnetism than electricity since the force lines and the poles behave much like magnetism than electricity.

For example, the negative mass pole doesn't exist in isolation. It exists only with the rotational motion of the source much like the magnetic current. Like in magnetism, it always exists in pairs with the positive mass pole.

So I guess there is a duality of the characteristics on this phenomena. It's magnetic in property but it came out of the womb of the single monopole(electric like) gravity in its origin.

Reflections on Lens-Thirring Force

In science, the force of tradition is powerful. A new drastic theory is always looked at with great suspicion no matter how it may sound correct or explain the nature so well. I think it's in human nature. There is nothing strange about it.

Still, it is so remarkable that Lens-Thirring force has never been challenged on its accuracy in regard to the direction of the force. Of course, the reason is because it amalgamated Mach's principle with general relativity so well.

It's like, of course, it should be. Everybody knows there is centrifugal force in nature and general relativity should be able to confirm it and moreover Mach said it is the result of the local rotating object in interaction with the rest of the matter in the universe.

Why would anyone want to challenge such a perfect scenario?

May be the crucial reason for this was because there was no cosmological or experimental data associated to their result at the time of their publication. There was no other guiding principles that can direct their mathematical results. Mach's principle was the only relevant light house, which in a sense had little to do with any empirical data.

Since Lens-Thirring force is basically the force caused by the circular acceleration of the individual mass components within the spherical shell(which is modeled as the universe), which comes from the fundamental postulate of general relativity, ie, an acceleration of a mass creates gravity effect, their result should not be different from the one calculated from the dipole gravity method using the relativistic center of mass shift of the rotating hemispherical shell.

They are basically the same forces.

As such, as the second strongest gravity force in nature, it should be able to explain cosmological phenomena hitherto unexplained. The unexpected obstacle in this effort was the obvious conflict between Lens-Thirring force and the supposedly attractive radial force in the equatorial plane in the rotating galaxy. The dark matter problem demands attractive radial gravity force in the galactic plane but Lens-Thirring force which is the small footprint of the same force at the center of the rotating center has the wrong sign because Lens-Thirring force is the outgoing force from the center as the centrifugal force is like.

What if Lens-Thirring force had come out with the opposite sign that is the correct one? First of all, they would have been disappointed by the result itself. And they would have abandoned the whole idea of publishing it. It's a very interesting speculation.. But I'm sure it could have sparked more debate and deeper investigation into the subject.

The question still remains is then what is the real cause of the centrifugal force? In mechanics, it is caused by the tendency of an object trying to stay straight line in circular motion. I don't know if an object requires the existence of all the other matters in the universe to make it want to go straight line to conserve momentum.

Probably not.

There may be other causes of this. Maybe the inertial ether effect. The reason a balloon tends to stay in the same spot when there is no wind blowing is because the total sum of the air molecules trying to give it a net momentum cancels out. It resists motion when it is pushed because of the canceling forces from all the molecules in the air. So, the cross section, the mass and velocity of the air molecules take part in this resistance effect.

Therefore, it becomes natural to speculate that there may be particles working like these "air molecules" for the gravity effect in the universe.

We can go on into this topic further, but it will take us to too far afield.

Sign Error in Lense-Thirring Force?

In the original paper published by Lense-Thirring, the sign of the radial component of the force in the direction perpendicular to the rotation axis was repulsive and harmonic which has been considered as the general relativistic confirmation of the centrifugal force and the Mach's principle. In his paper published in 1999, Jeong also used the result of Lense-Thirring to confirm that his calculation of the superposed dipole gravity force inside a rotating sphere matches with the previoulsy published results of Lense-Thirring.

However, after a careful investigation of the dipole gravity potential and comparing it with the observed cosmological data, it has been found out that there may be sign errors in both Lense-Thirring and Jeong's forces originally published in 1999.

In Lense-Thirring's case, obviously, it was their desire to prove that general relativity conforms to Mach's principle or vice versa. In Jeong's theory of dipole gravity case, it was his desire to make sure his result conforms to Lense-Thirring's in his presentation of the diagram.

It may be that both have been wrong in the signs of their forces.

The major reason for this suspicion is in the direction of the radial component of the dipole gravity (gravito magnetic) force in the equatorial plane. If the lines of the force resembles that of two opposing bar magnets within the sphere, the radial force line will be outgoing (repulsive) around the equatorial plane just like the way Lense-Thirring force behaves near the center of the sphere. And it should be that way if anyone wants to claim it is the evidence of the centrifugal force.

However, the problem with this is in the fact that the direction of the outgoing radial force in the equatorial plane is not consistent with the dark matter problem. Also at the poles, the direction of the dipole gravity force is incoming which makes it hard to explain the jets considering that the Newtonian gravity force line is also incoming. So, the jet phenomena can be explained more logical way if the Z directional potential is like below than its upside down form.



For example, in the above shape of the potential along the Z axis, where the domed side represents the repulsive force, any density overflow from the central region toward the poles will be automatically ejected along the rotating axis of the space. And the longer range Newtonian gravity will bring them back to form two way jet streams. The only problem with this reversion is that the original Lense-Thirring force has to have its sign reversed.

While the direction of the dipole gravity force can be made arbitrary, because the direction of the center of mass shift can be defined either way depending on the convention, it has to be consistent with the observed cosmological data.

To solve the dark matter problem, we need an additional long range radial gravity force in the equatorial plane that is not repulsive but attractive. If this is the case, Lense-Thirring force has its sign reversed.

The derivation of the radial force in the equatorial plane presented in the page has the correct sign, because it was derived directly from the original potential not read off from the diagram.



In the illustration above, the force lines at the center of the two superposed gravito magnets are incoming(attractive) and that of the both poles of the magnet are outgoing(repulsive). At the center of these two magnets facing the same type of poles(attractive) in the middle, the force lines along the equatorial plane will form array of horizontal incoming force lines. The extension of this force lines at the center between the two gravito magnets can not be outgoing, meaning that the following expression of Lense-Thirring force has the wrong sign(remember the centrifugal force is radially outgoing force ).


The fundamental physical reason for this is because the continuity of the force line either in magnetism or gravito magnetism doesn't allow the change of its direction on its path 180 degree.
Therefore, Lense-Thirring force has to be the attractive harmonic force toward the center in the equatorial plane in total contrast to their original claim and also the force along the rotation axis must behave like repulsive harmonic force as shown in the above potential diagram along the Z axis(notice the potential near the center(Z=0) of the diagram) instead of the attractive harmonic force shown in the above expression and in the previous saddle diagram.

This comes to the clear conclusion that Lense-Thirring force has nothing to do with the centrifugal force. It is rather a simple manifestation of the attractive radial dipole gravity force near the center of the rotating spherical shell.

Therefore, it is corrected at this point that the dipole gravity force in the rotating hemisphere is attractive on the flat side and repulsive on the domed side, instead of the other way around. It makes the jet phenomena explained in a much more simple and elegant way and so is the dark matter problem, although the way the dipole moves itself in space makes it not being very well stream lined in the normal common sense of the aerodynamics.

But then there is nothing common sense about cosmology anyways. The alternative method of detecting dipole gravity force experiment mentioned in the following page will prove on this point by showing the direction of its actual movement in space.

Now, it seems that the overall consistency is restored.

Let's blame it on Mach. It was all his fault. :)

Of course, I'm trying to be humorous here if anyone has noticed. It's Lense-Thirring's fault and Jeong's fault as well when he modified the dipole potential diagram to fit the result of Lens-Thirring's. But how about those who didn't check it out all the way through? Let's try to be happy at least we found the error and corrected it.

Pedagogy on Dipole (Anti)Gravity

For those who are not familiar with the origin of dipole gravity, it would be informative to quote from a textbook on gravitation. The following is a clip from the book by A.K. Raychaudhuri, S.Banerji and A. Banerjee titled "General relativity, Astrophysics, and Cosmology". There is no special reason for quoting from this book, because it is the same in "Gravitation" by Kip Thorne et al. as well.

Linear expansion in mathematics is a convenient way to sort out a major complex function into a series of simplified terms in the order of its magnitude or around the region of particular interest. The first major term in the weakly gravitating linearized theory of general relativity which is the strongest is Newtonian monopole and naturally the second one is the gravitational dipole.



The above is quoted from the chapter on "External field of a weakly gravitating source" on page 43.

"The dipole term vanishes, if the origin O is also the center of mass of the source" is what it says and agreed upon. The integral is basically the definition of the dipole gravitational moment that is the length element times the density integrated over the whole volume of the object. It must be noted that this is a very broad general statement regardless of the geometrical shape of the source in consideration.

However, when the rotating hemisphere is introduced as a source, it becomes obvious that the meaning of the statement "if the origin O is also the center of mass of the source" becomes very ambiguous. Although the standard choice of the geometrical shape of the source has been a sphere since it is generally the easiest and the simplest shape to integrate the Newtonian potential over the volume element, this doesn't necessarily have to be the case for the dipole gravitational moment.

Now the question is "which center of mass?" since the rotating hemisphere now has the duality in its center of mass. The one at rest or the one in rotation? If one had set up the origin of the coordinate system at the center of mass of the hemisphere when it was at rest, the new center of mass in rotation would have been shifted due to the relativistic mass increase effect. One may say the origin of the coordinate system has to be the one that has already been shifted. But the problem is not that simple, because no one asks how fast the object is going to rotate before setting up the coordinate system. And furthermore, this question did not exist for the rotating sphere. Why?

This shift is energy dependent and it's not a fluke of accident caused by the misaligned coordinate system. Here we postulate that this relativistic center of mass shift is the real cause of the gravitational dipole moment.

However, it must be noted that even without this postulate, if Lens-Thirring had their calculation using the rotating hemisphere, they would have gotten the same answer. They could have come up with all the details of the dipole gravity field around the rotating hemisphere. The reason for their result which covers the region only close to the center of the sphere was because of the wrong choice of the (gravitational) source(spherical shell). If one chooses the rotating sphere as the source, the integral calculation for the dipole gravity field becomes very difficult other than the region close to the center of the sphere.

It seems like the unique way a finite length element can be related to the rotational motion of an object is by the relativistic center of mass shift from the rotation of a longitudinal axially asymmetric object.

In any case, the rest is to see if the result of this "postulate" conforms with the known results in physics, for example, Lens-Thirring force etc and furthermore, to see if the results can explain cosmological phenomena hitherto unexplained, ie, jet phenomena, dark matter problems and others.

The importance of this force is that it is the strongest long range gravity force right next to Newtonian gravity. And any other higher order gravity effect will be weaker at least by the factor of v/c.

Some time ago, there was a debate regarding the theory with Dr. Choptuik at UT Austin. It must have been almost 9 years ago. He said "dipole gravity is not general relativity". He may be right because Einstein did not say anything about it. In fact, if you have special relativity, and apply it in the same manner to any advanced theory of gravity(for example, Brans-Dicke theory of gravitation), the second order linearized term will show the same result ie, dipole gravity. So, in a way, dipole gravity does not help differentiating general relativity from other similar theories.

However, is it really fair to say dipole gravity is not general relativity? I don't think you can say DPG is not general relativity. But then also, you can't say it is the trade mark of general relativity either. After all, Newtonian gravity can be derived out of both general relativity and Brans-Dicke theory solely because they are designed that way. If your theory doesn't produce Newtonian gravity in its linearized form, your theory of gravity would be simply wrong.

If you say "dipole gravity is not general relativity", isn't it the same as saying "Newtonian gravity is not general relativity" as if Newtonian gravity has nothing to do with general relativity, which is not true. Both Newtonian gravity and dipole gravity are parts of the broader theory like general relativity and/or Brans-Dicke theory. However, neither of them(NG and DPG) may provide the crucial test to differentiate between the two( general relativity and Brans-Dicke theory).

Dipole gravity is a part of general relativity and is also a part of Brans-Dicke theory as well. It is a theory that can not be avoided once special relativity is proven to be correct. Apparently, the rotating hemisphere violates Newton's second law of motion. Because its center of mass changes without the external force in the direction of the shifted center of mass.

We can not take both principles to be absolutely correct when they are contradicting each other in such a glaring fashion. http://dipoleantigravity.blogspot.com/2007/05/what-is-at-stake.html

Gravity Probe B Raw Data

The GPB probe may have already enough raw data to prove the theory of dipole gravity(gravito magnetism). Some of their anomalous results have been put aside as being caused by some kind of electrostatic disturbance effect present within the device itself.

But with such a high precision device that may have been already tested in the laboratory numerous times, it is hard to believe it can have such a systematic error that has not been expected before hand.

And most importantly, how would they know if their device is performing properly or not without a proper theory that predicts physical anomalies that are measurable within their range of precision. After all, gravito magnetic(dipole gravity) effect is the largest right next to the Newtonian gravity.

As such, any huge unknown anomaly in the raw data must be associated with this effect, ie, the true gravito magnetism based on dipole gravity, not the one based on the modified Maxwell's equation.

Investigation of this possibility by analyzing the raw data can be an excellent PhD dissertation project.

Gradient of the Dipole Gravity Potential

In the following we will discuss the gradient of the dipole gravity potential. This shows the detailed picture of the actual force associated with dipole gravity. This program is accomplished by taking the gradient in the spherical coordinate system on the isolated dipole potential.



where the function f is replaced by the following expression which is the total gravity, ie, the Newtonian gravity plus the dipole gravity for a rotating hemisphere.





In the case of the radial component(r dependent force) of the dipole gravity force,

,

where dz is the gravitational dipole moment and the latitude angle theta is measured from positive Z axis of the rotation. Since the center of mass moves toward the flat side of the hemisphere while in rotation, convention has to be made in such a way that the flat side of the hemisphere faces the positive Z axis.

The value of the cosine function changes its sign from positive to negative as it crosses over the equatorial plane of the rotating hemisphere, which is located at half the length of the radius down from the flat side of the hemisphere toward the dome, where the latitude angle is 90 degree.

This is the fundamental cause of the repulsive gravity force at the domed side of the rotating hemisphere and the unidirectional acceleration of the isolated dipole gravitational moment in the matter filled universe and also the justification for the experiments proposed in

http://dipoleantigravity.blogspot.com/2007/04/alternative-method-of-detecting-dipole.html

and

http://dipoleantigravity.blogspot.com/2007/04/testable-prediction-from-rotating.html.

It must be noted that this is the same force that produces the Lens-Thirring force near the center of the rotating sphere when the two rotating hemispheres are superposed face to face to form a single rotating sphere.

The latitude angular dependency of the dipole gravity force



is represented by the force in the direction from the flat side of the poles toward the domed side following the latitude circular curvature of the radius r. The strength of it is maximum at the equatorial plane which is at the 90 degree latitude angular position and it is minimum when the latitude angle is either at zero or 180 degree.

At this point, it must be noted that the directions of the force lines resemble exactly that of a dipole bar magnet. In all the similarities and qualifications, this is the gravitational dipole magnet as stated in the introduction, the true "gravito-magnetism" that has been searched for a long time.

After all those effects and calculations, there is one new physical entity stands out, that is this new negative gravitational mass pole on the domed side of the rotating hemisphere which exists temporarily with the angular momentum. Since the angular momentum is conserved, the negative mass pole doesn't disappear as long as the angular momentum stays on. It can also be seen that this negative gravitational mass pole can not exist in the universe in isolation.

The last phi(circumferential angle) directional dipole gravity force is zero because there is no phi dependency in the dipole gravity potential.

We don't know exactly what it means when people say "frame dragging force" in terms of its mathematical form, but at least there is no "dragging" force that follows the rotating surface along the circumferential direction(phi direction) within dipole gravity which is the strongest gravity force next to the Newtonian monopole force.

This term is normally used in association with Lens-Thirring force but its strength is v/c times smaller compared to the radial dipole gravity force. Lens-Thirring force is certainly a part of gravito-magnetism(dipole gravity) but "frame dragging force" is too weak(V/c) to be a part of it. If Gravity Probe B works perfectly, it will detect dipole effect in a much more stronger signal before it detects the "frame dragging" force.