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.

How Did It Begin?

I do not seriously believe there is such a thing as serendipity. I tend to beleive it is a consequence of the unending pursuit for the quest for the truth of the nature. The process of finding it doesn't stop in our conscious memory. Subconscious mind takes over and continuously seeks for the answer even while we are in sleep. When it finds all the clues relevant to the subject question and links between them, voila you have the answer. Nothing happens without reason.

While studying physics at the Rackham graduate school of the University of Michigan, Ann Arbor, I was interested in the quark confinement problem. I devised some phenomenological quark potential using the result from the renormalisation group equation and also by introducing the simple transformation between the scaling factor and the length element. The result was interesting. One of the interesting consequence of the finding was that the ratio of the mass of an electron from QED and the mass of a quark from QCD turned out to be 1830, which happens to be about the ratio between the mass of an electron and a proton. The ratio could be obtained because the infinities in the form of 1/(n-4) ,where n denotes dimension, factors out from both QED and QCD within the dimensional regularisation scheme in quantum field theory. Dr. Veltman's lecture on dimensional regularisation was brilliant, inspiring and filled with energy. The measured coupling strengths predicted the mass ratio of the two most stable elementary particles. I thought it was a very exciting discovery. It may have proven that the infinite quantities (eg, mass of the elementary particles) quantum field theories provide to us are not exactly infinities and also the universe may not be exactly in the four dimensional space.

In the course of the liberal thoughts and day dreaming about the nature at the beautiful campus in Ann Arbor, I always felt that there was something missing about our knowledge on gravity that it is not complete or there is something missing in our understanding without having any idea on what it may be. I remember taking a look at the text book on gravitation at the library to see if there is anything beyond Newtonian gravity. However gravity was not my main subject of interest at this time. I was interested in the theoretical high energy physics. The most puzzling experience in this episode was when I looked up the page describing the linearized form of general relativity. There was something next to Newtonian gravity and that was the dipole gravitational moment. And it was dismissed by a reason that I thought was too much of tongue in cheek argument. The fact that one has to move the origin of the coordinate system to the center of mass of the object to remove the term seems too convenient or/and unnatural(can't find the right word for it) because one can always set up the origin of the coordinate system at the center of mass of the object and forget about the coordinate alignment problem. I thought it was an unnecessary and non physical activity and it may hide some more serious physics involved. But there was no way I could have guessed at the time that it could have something to do with the anomalous center of mass shift from a rotating hemisphere. In 1995, the puzzle was solved after 13 years since I was wondering about the gravitational dipole moment. It happened when I asked the following two questions in my mind. What is so special about rotating hemisphere? And then how about the center of mass? Answers to these two questions answered the 13 years old questions in my mind. The gravitational dipole moment. It looks like there is no way we can avoid this solution. As it turned out later, the jets and the dark matter problem are the two different sides of the same coin due to the dipole gravity effect from the fast rotating black hole.

What is so peculiar about the jets from the black hole accretion discs it is that the normal gravito magnetism can not work simply by observing the fact that the jets are coming out of both sides of the axis not from only one side. So it must be completely different from the simple "gravito magnetism" in analogy to electricity and magnetism. Rotating mass may create gravito magnetism but not in such a simple way as one would expect a charged sphere would create a magnet by its rotation.

And then there was a popular issue of the jets from the black hole accretion disc at the time. I didn't believe jets could be explained by plasma and the surrounding strong magnetic field, when the event horizon was defined as the line that can not be crossed even by light. It was to me a monumental self contradiction. I couldn't believe how people could be bought into it. I remember thinking to myself that if there was any force that can make jets possible, it must be some kind of gravity but not electromagnetism.

I met Dr. Donald Hinson at the UT lab after I came back to Austin and asked him if he could plot the potential diagrams and the result was the beautiful quadrupole gravity potentials and the saddle diagram. Since the first result didn't come out in such a way that it was consistent with Lens-Thirring force, I told him to fix it to match with Lens-Thirring's. It was plotted using the reversed sign from the original mathematical form of the potential.

Still, anyone could tell there are jets on both sides of the poles of the rotating ultra compact stellar objects just by reading the potential diagram. The result was published in the journal Physica Scripta in 1999 . As anyone may have guessed, it was not easy to make it published as it was a humongous heresy in the gravitational physics community at the time and as it may still be now. It should have gotten a space in Physical Review Letters.

The identity of the dipole gravitational moment has been hidden from the plane view for the last 90 years since the birth of special relativity. In a way, this problem should(could) have come out to question the compatibility between Newtonian mechanics and special relativity in a much earlier time. It could have been a serious subject of debate. If it did, the gravitational dipole moment would have been discovered much earlier. There may be people who tend to think that gravitational dipole moment would have been such an easy thing to discover. But for the last 90 years, out of the total population of the earth lived in that period of time with so many talented geniuses in the physical and scientific field of the world, I thought to myself, from time to time, why it had to be on my table. I was not talking until late compared to other kids and it concerned my parents. And my questions bothered adults in the family that they always had to hush me down from asking too many bothersome questions when I was a little boy. My sister knows how I was called in the family which I'm not going to reveal to protect my dignity. My sentences don't finish right when I'm writing. My thought process has wild disconnected jumps from one subject to another with totally different issues as anyone may have guessed in this blog. I'm not a good writer and never felt I could write anything more than a few sentences or paragraphs without totally confusing the reader on what I'm really trying to say. It's all there but it takes a long while to get it all together. I always wondered how anyone could write a book with thousands of pages without repeating the same story or content over and over again. I truly admire them all who do. If there is anything that I may have done to deserve it is that I never stopped asking questions and asked the right question at the right moment. The answer is not always immediately obvious but our brain is such a marvelous thing that it works hard day and night to provide the answer to the one who seeks it.

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 Lense-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.

Radial Component of Dipole Gravity Force in the Equatorial Plane

To calculate the length of the jets from the rotating sphere solely from the linearized theory, one can simply use the following potential.



To find the distance r that makes the above total potential zero on the domed side of the rotation axis using the fact that the maximum length allowed for the relativistic shift of the center of mass is R/2 where R is the radius of the sphere(see below diagram), the distance r that defines the length of the jets becomes barely an order of the radius of the sphere R.

http://www.tachyonics.com/9604044.pdf .

This is not enough to account for the observed length of the jets. There are many factors that may affect this outcome. The actual geometrical shape of the rotating center could be one of the main factors. If the galactic center is no longer shaped like a sphere but widely stretched disk shape in its solid structure, it will certainly affect the length of the jets in such a way that it extends further away from the center.

There could also be a significant contribution from the non linear effect that the linearized theory could not have taken it into account because the system will no longer be in the weak field regime.

At least for the time being, for the purpose of simulation as a cosmological model , one may have to use the dipole moment (mass times the center of mass shift) as a parameter that determines the strength of the jets. This may eventually help determine the actual geometrical shape of the galactic center.



The radial component of the gravito magnetic force around the equatorial plane in the above has M delta Rc dependency which is the major parameter in determining the length of the jets. Here, we can see that the experimental correlations can be made between the length of the jets and the parameters that determine the velocity curve in the dark matter problems of cosmology.