Sunday, December 30, 2007

Questions on the Covariance of Dipole Gravity

It seems that this subject is a lingering question to many of the readers of dipole gravity. When a new metric is devised, this certainly becomes an important issue. A fully covariant field equation was expanded in the linearized theory and expressed by sums of infinite number of the individual multipole components. So in reality, the individual poles(monopole, dipole, quadrupole...etc) are not covariant by themselves, the total sum is. In other words. dipole gravity can be formulated only in the asymptotically flat space time region. However this argument can not be used to underestimate the importance of its physical implication. Just like Newtonian gravity is a solution of general relativity in the asymptotically flat space time region, so is dipole gravity. The most important aspect of it may be its unique topology.

Even so, it is amazing to see how much of the cosmological mysteries are solved solely by Newtonian(monopole) gravity. As the energy scale of the cosmological system gets larger, the higher order of the poles start making important contributions. The reason Newtonian gravity could not explain the jets and/or the dark matter problem was, in retrospect, because we have been working with a totally simplified, truncated non covariant field. As the more of the higher order poles are included, the overall gravity field starts becoming more accurate and offer solutions to many other mysteries of the universe. Since the strength(magnitude) of the each poles decrease by the factor of c (speed of light) as the order increases, after the inclusion of the second and third terms of the linearized theory the overall sums of the field will still be accurate enough to cover most of the observable universe.

So, one can view the overall scheme of the linearized theory of general relativity by the following; the spatial translational motion is covered by Newtonian gravity(via point mass approximation), the intrinsic rotational motion of the bulk object is covered by dipole gravity and finally the intrinsic vibrational motion of the extended object is covered by the gravitational quadrupole moment.

In retrospect, I always felt that there was something fundamentally missing in our understanding of the universe. I remember looking up the text books on gravitation in 1982, even though I was not an astronomy major when I was a graduate student at the University of Michigan Ann Arbor. 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 seemed 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 which may hide some more serious physics involved. The reason for its dismissal, I thought, was too frivolous compared to the possible importance of the term.

Because if general relativity have answers to the further mysteries of the universe, it should be in the term next to the Newtonian gravity in the linearized theory.

The conventional treatment of it made me feel suspicious of the argument. I never trusted any derivation of the physical equations in the text books in my college years until I derived it myself anyways.

It's like weighing a feather same as a gold nugget painted like a cotton.

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 the rotating hemisphere. In 1995, the puzzle was solved after 13 years since I began wondering about the strangeness of displacing the origin of the coordinate system to remove the dipole term in the linearized theory. It happened when I asked the following two questions in my mind. What is so special about the rotating hemisphere? And then how about the center of mass? The answers to these two questions answered the 13 years old questions in my mind. Hermes struck me down at the instant. The gravitational dipole moment!!!! It looks like there is no way one can avoid this solution. 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 holes.

At the moment, the quadrupole gravitational moment seems to be the main interest of experimental investigation in gravity. However, we missed dipole gravity altogether and there is no doubt that it should be investigated fully in the near future especially because it is much more stronger than the quadrupole moment. The extensive investigation of dipole gravity will determine the scope of the overall success of Einstein's initial revolution.

After that, when we still have too many mysteries remain unsolved, the next order of the poles will offer important clues to the problem. In this respect, the quadrupole moment will become important in the much high energy scale than that of dipole gravity, so we may be too far ahead of our steps in the adventure to the cosmological mystery.

In regard to this subject, if we assume that a big bang occurs in a much higher energy scale than that is governed by dipole gravity, it is quite conceivable that the instability arising from the vibrational oscillation of the quadrupole moment can result in the massive disintegration of the black hole in the form of a big bang. So, the extreme relativistic extension of the gravitational quadrupole moment can be a big bang which is listed as a question mark(?)in the dipole gravity chart.

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