"Inertial Dragging in the Collapsed Universe"
Todd Murphy, 2016. Email
The prevalence of rotation in the universe, and recent evidence 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 (1, 2). 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), yeilding a Newtonian derivation of the Schwarzschild Radius.
I offer the suggestion that high-velocity special relativistic effects operating, not on the collapsed 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 the rotation of it's gravitational field reached the angular equivalent of the velocity of light might include a 'cancelation' of gravitational effects just as temporal effects stop at it's linear velocity. Release of the potential energy bound in the hyper-compressed mass of the universe might account for it's expansion.
In another scenario, should the angular velocity for inertial dragging exceed that of light, then the possibilty appears that the collapsed mass of the universe might be affected by gravitation in the opposite (outward) direction, just as time goes backward for a mass with a velocity greater than the speed of light.
The effect would be to radiate the mass of the universe outward in all directions, at tangents to positions on the event horizon at the time the radiation took place.
Both scenarios (rotation of the gravitational field at the velocity of light, and exceeding that value) posit expressions of Special Relativistic electrodynamics in a General Relativistic context, and require mathmatical models outside the scope of this brief communication.
In either model, the mass of the universe would tend to move outward on tangents to the escape horizon. The bulk of the universe's mass would tend to be attracted to itself, following long elliptical orbits around its center of gravity, unlike the stricly radial expansion implied in Hubble's classical cosmology. Indeed, there is recent evidence that the universe is rotating.
Such a distribution for the universe's mass would make an open-ended expansion improbable.
Postulating that there was inertial dragging in the rotating gravitational field surrounding the collapsed universe leads to the conclution that we live in an oscillating universe.
1) Cohen & Brill "Rotating Masses and Their Effect on Inertial Frames" http://journals.aps.org/pr/abstract/10.1103/PhysRev.143.1011 Physics Review Letters, 25 March 1966 (link)
2) Cohen, J.M. & Brill, D.R. "Further examples of "machian" effects of rotating bodies in general relativity" Il Nuovo Cimento August 1968, Volume 56, Issue 2, pp 209–219 (1968) 56: 209. doi:10.1007/BF02710148 (link)
Acknowledgment: The calculations were done by Carey C. Briggs (formerly of the Harvard-Smithsonian Center for Theoretical Astrophysics), using the author's specifications.