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The Second Order Term in the Linearized Theory of General ‎Relativity, Dark Matter and Related ‎Cosmological Mysteries

The blackhole jets, Saturn ring, dark matter and GPB anomaly are generally considered unrelated physical mysteries that have no common causes that create them. In Newtonian mechanics, the center of mass of an object change only when there is an external force applied to the object. However, the longitudinally asymmetric and radially circular (LARC) rotating objects like cone, funnel, and hemisphere have a unique mechanical property of creating a finite shift of relativistic center of mass depending on the speed of the rotation due to the difference in the instant speed of the individual mass components of the object while in rotation (Jeong, 1996). This suggests that the LARC rotating object has a complex mechanical property that does not obey the conventional Newtonian mechanical principle. It turned out that in the weak field limit of general relativity there is a second order mathematical term that requires a finite shift of the center of mass to establish its physicality. This term was discarded as physically meaningless because spherical source does not develop a shift of the center of mass even in rotation due to the mathematical cancelation. It is shown that the relativistic shift of the center of mass from the rotating LARC object is the cause of the physically meaningful dipole gravity that reduces into Lense-Thirring force at the center of the rotating spherical shell. However, after careful examination we found out that the signs of Lense-Thirring forces were reversed and once the signs are corrected, dipole gravity predicts blackhole jets and the flat rotational velocity distribution curve which is the key evidence of the existence of the dark matter. We presented that the rings in Saturn, Jupiter, Neptune and Uranus, the GPB experimental anomaly are also the results of dipole gravity from the rotating spherical sources.