Tuesday, February 2, 2010
The first term is the Newtonian gravity and the second term is dipole gravity where the information regarding the rotational frequency and the geometrical shape of the object are included in the parameter "delta r" which is the relativistic dynamic shift of the center of mass. The direction of the shift vector of the center of mass is toward the direction where it moves away from the stationary state.
Note that the traditional interpretation of general relativity did not allow us to include this information regarding the rotational frequency. So, general relativity could not be used to explain any of the fast rotating cosmological objects. And most of the problems related to the fast rotating cosmological objects including the spiral galaxy was begging for explanation. This is one of the reasons we have MOND and other phenomenological theories to explain them.
For a rotating full sphere, we have to add another hemisphere in the opposite direction to the one above. Since the potential function is a scalar quantity, we can add as many units of dipoles as far as their coordinates are adjusted with respect to the one single coordinate system.
If you fold two dipoles in the exact opposite direction, at the identical center of mass, the dipole effect will be canceled. However, remember that the center of mass of the two hemispherical dipoles in a single sphere are separated by the distance r (in the rest state).
So, they do not cancel in a rotating sphere.
We can now see that the poles of the fast rotating spheroidal condensed objects can be strong repulsive(antigravity) gravity centers.
This effect can cause the phenomenon of the hollow poles and the rings of the Saturn, as well as the observed jets from the fast rotating neutron stars and also from the fast rotating black holes.
This effect can also cause the stationary communication satellites to oscillate back and forth from the equatorial plane of the Earth which has been observed and by now a well known fact due to the GPS misalignment problem.
The equatorial plane of the fast rotating cosmological body is a shallow potential dip of dipole gravity which causes the debris and the satellites to oscillate back and forth around this potential dip. As the debris lose kinetic energy due to the collision and other frictional effect, they will permanently settle down at the equatorial plane to form the layers of the rings.
Sunday, January 31, 2010
Pardon, Dr. Jeong, but I was looking into your discussion into dipole gravity and came upon particular objections that I was hoping you'd be willing to field for me.
Q: 1. An object's gravitational dipole is a measure of how much that mass is distributed away from some center in some direction. It's a vector, since it had to convey not only how much the mass is off-center but also which way. Considering some object in the abstract, the natural 'center' to pick is the center of mass, which is the point around which the dipole is zero.
A: The gravitational dipole moment cannot be defined in the classical mechanics because the center of mass can be made to be the center of the coordinate system at all times, if we are allowed to discuss it in the context of the linearized weak field limit of general relativity. So, there is no meaning of dipole gravity in the classical Newtonian mechanics. That's why there is no known definition of gravitational dipole moment in the known theory of gravity. However if we try to define gravitational dipole moment in comparison to the electromagnetism, one has to have a negative mass which is not a physically meaningful object. Because of this, we are always reminded of the fact that gravity is not the same as electromagnetism. They do not operate with the same physical principle.
Dipole gravity is a solution of general relativity that provides the answer to the origin of the Lense-Thirring force. Therefore, it provides the correct definition of the gravitational dipole moment, that is, it is the mass times the dynamic shift of the center of mass caused by special relativity due to the specific geometry of the object and the speed of rotation .
Q: 2. Oscillating electric dipoles radiate electromagnetic waves. But for gravitational radiation you need an oscillating quadrupole moment. The difference is that electric charge comes in two varieties of charge, plus and minus. When you interchange the two charges, as in an oscillating electric dipole, you get a change in the electric field distribution. Gravitational mass, on the other hand, comes in only one sign: plus. There are no minus values. So if you interchange two masses you don't get a change in the gravitational field. Hence, no dipole radiation.
A. Dipole gravity is a static field, it doesn't radiate. It exerts force on a stationary object. It is an another reminder that gravity is not the same as that of electromagnetism. On the other hand, gravitational radiation may come from the time dependent quadrupole field.
Q: 3. Another way to see this is as follows. Radiation comes from accelerating sources. When a quadrupole rotates, there is the usual acceleration associated with rotation. A dipole depends on the displacement of the center of mass from some fixed point. The velocity of the center of mass is simply given by the total momentum divided by the total mass. Since each of these quantities is conserved, the velocity of the center of mass doesn't change. In other words, it doesn't accelerate. So there's no dipole gravitational radiation.
A: Again, dipole gravity is not radiative. The general results of electromagnetism can not be blindly assumed to happen in gravity.
The conventional gravitomagnetism is the result of the same misunderstanding regarding the property of gravity and the wrong assumption that somehow gravity and the electromagnetism may/could be very similar.
---In general, an isolated gravitational dipole moment can not be localized, which means that it is a perpetually accelerating object due to the gravitational interaction of itself with the rest of the universe, which obviously can be the key to the problem of the space adventure.---
I hope this could clarify your question.
Anything you could tell me would be greatly appreciated.