Inertial Dragging in the Collapsed Universe
Todd Murphy, 2001
The prevalence of rotation in the universe makes the postulate that the collapsed universe was rotating previous to the Big Bang seem reasonable. Even though the mass of the universe may have been collapsed to a singularity, so that it's rotation becomes difficult to contextualize, there is still the rotation of it's gravitational field to be considered.
The rotation of gravitational fields has been termed "inertial dragging" and has been explored by physicists J.M. Cohen and D.R. Brill. The following equation gives the angular speed of rotation of inertial frames. at a distance R from the center of a rotating mass of angular velocity J Where omega is inertial dragging, G is the gravitational constant, and c is the velocity of light in vacuo.
According to Newton's law for centrifugal force, a body in circular orbit around a mass M at a distance R from the center will have a linear escape velocity when:
V2 = GM/R (V2 = velocity squared)
will have an escape velocity equal to the speed of light when
M/R = C2/2g (C2 = square of the speed of light)
Since the square of the escape speed is twice the square of the circular orbit speed.
This implies that R=2GM/C2 (C2 = square of the speed of light)
I offer the suggestion that high-velocity special relativistic effects operating, not on the universe's mass, but rather on it's gravitational field, might 'stop' gravitation when the field's inertial dragging reaches the angular equivalent of the velocity of light.
At the velocity of light, time stops, and matter is compressed into radiation. If gravitation were to demonstrate similar effects, the range of phenomena that might appear when it's inertial dragging reached the angular equivalent of the speed of light might include a 'stopping' of gravitational effects just as temporal effects stop at it's linear velocity.
Should the angular velocity for inertial dragging exceed that of light, then the possibilty opens that the collapsed mass of the universe might be effected by gravitation in the opposite direction, just as time goes backward.
The effect would be to radiate the mass of the universe outward in all directions.
Recalling that the mass of the universe would tend to travel outward on tangents, so that the bulk of the universe's mass would tend to be attracted back to the center, following long elliptical orbits around it.
Such a distribution for the universe's mass would make an open-ended expansion very unlikely.
Assuming inertial dragging in the collapsed universe leads to the conclution that we live in an oscillating universe.
Cohen & Brill
"Machian Effects of Rotating Bodies in General Relativity"
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