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Closed Time Like Curves in the Dark Matter Galactic Halo?
Globally flat Minkowski space has a finite conformal image on the
Einstein static universe "cylinder." Similarly for DeSitter dark zero point energy space /\ 0 with negative pressure making a cosmic antigravity repulsive field accelerating the expansion of 3D space from the initial "singularity", for dark matter Anti-DeSitter space with /\ 0, positive pressure and closed timelike worldline as in Godel rotating universe and for Bondi-Gold "steady state universe." Closed timelike worldlines in the dark matter Galactic Halo? All these solutions have different finite conformal images on the above archetypal "Einstein cylinder." The boundaries of these images are "infinities" of various kinds. The Big Bang may not be a singularity in sense of infinite curvature, but rather a vacuum ODLRO phase transition in which curved spacetime as a smooth number geometrodynamic field emerges. That is the identity tetrad action on the tangent bundle is the local scalar Cartan IT 1-form e = I + A A encodes all the geodesic deviation curvature information from A ~ Theta/\dPhi - dTheta/\Phi F = dA ~ dTheta/\dPhi Theta & Phi are the 0-form macro-quantum coherent Goldstone phases of the World Hologram that encodes all curvature BITS in the three real component Higgsian vacuum ODLRO inflation field that may be related to electroweak symmetry breaking giving an effective Planck area of 10^-32 cm^2 rather than 10^-66 cm^2? If A is Abelian U(1) dF = 0 d*F = *J(source) d*J = 0 (local conservation of source currents in goemetrodynamic subtratum) * is Hodge dual if A is SU(2) electroweak D = d + A/\ i.e. A has two internal indices The Yang-Mills field equations in geometrodynamic substratum are F' = DA DF' = 0 D*F' = *J' D*J' = 0 Einstein's GR is recovered from e = eu^adx^u&a = e^a&a ds^2 = e^a(Minkowski)abe^b This is Einstein's equivalence principle in Cartan tetrad formalism. That is, geodesic observers are weightless. Pure gravity force is always zero. It is eliminated in Einstein's GR. Non-zero pure gravity force only has meaning in Newton's theory. Whenever you pull g's and feel weight that is caused by a non-gravity force that pushes you off the geodesic of the curved spacetime you are in. Weight is always a reaction to a non-gravity force like when you stand on the surface of Earth, your weight is from the quantum electrical forces in the rock you stand on. When you choose a "hovering" or "shell" non-geodesic local frame (LNIF) by applying a non-gravity external force, then you get an accidental relation of the non-gravity force to the geometrodynamic connection field. The latter is not a tensor field. It adapts to the non-gravity force and locally vanishes when the non-gravity force locally vanishes. |
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