Reader's Feedback(Geometrical Question)

Some of the readers of the dipole gravity blog may wonder if I have received any private emails challenging the basic concept of dipole gravity. Since I have been speaking out openly regarding dipole gravity to the general public, I have received none. I openly invited for debates, but no one volunteered to come forward. I'll post any critical errors or mistakes in the presentation of dipole gravity pointed out by the readers in the blog.

One of the minor errors pointed out by one of the readers was about the location of the center of mass of a solid hemisphere. I used hemispherical shell for the dipole gravity model in the published papers, since a spherical shell was used by Lense-Thirring as a model in their calculation for the purpose of simplicity. It was a good starting point for the proof of concept.

In the case of a hemispherical shell, the center of mass is located at the point (1/2)R from the center of the full sphere. However, for a solid hemisphere, the center of mass is located at (3/8)R from the center of the full sphere. This was pointed out by one of the readers and I appreciate him for this correction. Somehow I have been assuming that the center of mass of a sold hemisphere at rest was at (1/2)R just like that of a hemisphere, which is not correct.

In the case of a fast rotating black hole, I have a serious doubt that the core of the galactic center will be spherical. It will be more or less like a two superposed funnels with long protrusions at the poles with a wider rim at the equator. The reason for this is because the equatorial plane at the rim will be bombarded by the incoming debris due to the dipole gravity force which is strong and relatively short ranged compared to the Newtonian gravity. The balance point will be achieved where the centrifugal force becomes equal to the dipole gravity plus the Newtonian gravity.

In the absence of the strong dipole gravity, a non-rotating stellar object will assume a spherical symmetry, naturally, due to the isotropic nature of the Newtonian gravity.

However, in the case where the dipole gravity is strong, the spherical symmetry will be broken and the shape of the fast rotating stellar object will assume a topology which conforms to the overall dipole gravity force lines, which is basically like a two superposed funnels attached face to face. The elongated shapes of the both of the polar axis can be anticipated due to the collision of the ejected matters and the incoming stream of particles which will eventually settle down in balance.

So, it is interesting to see how the Kerr metric for the rotating black hole has to be modified in this particular geometry, since the spherical symmetry was assumed in the original Kerr metric.