In Gödel's "Example of a New Type of Cosmological Solutions of Einstein's equation of Gravitation", all prior cosmological solutions with a non vanishing energy density have a property of all world lines of matter are everywhere orthogonal to a family of 1-parameter three-spaces (We know why) as a certain sense of "absolute" time coordinate. Given the manifold is Semi does not bother physics so much as far as I know but but Gödel utilizes it constructively: There are $10$ interesting properties enumerated by the Gödel. The 0th is equivalent to demanding the above property does not hold. All the rest are consequential mostly. Among all enumerated, the property he named totality of the entire set of the time-like and of the nulls into $+$ and $-$, interchangeability by negation, and that converging sequence of a single-type has that type (unless $=0$). So/Furthermore "universally" speaking there a linear order. But then either by construction or simply due to the surprising features of the manifold being a direct product of $\mathbb{R}$ (The ""innesential coordinate"") and a $(-,+,+)$ manifold there will be instances entirely inconsistent or in contradiction to the linearity. Etc,Etc....

Two very basic questions:

  1. Does it make physical sense to (diffeomorphically) add a patch somewhere in the "middle" of the space-time initiated for example by star formation and then evolution by manipulating locally the cosmological structure (According to and using only the existing features (both LHS and RHS are principally not changed)).

  2. Another interesting thing to try is add new global "artifacts" in the process. Makes Sense?

Or, astronomical formations and processes only make analytical sense within their own dedicated space-time?

  • $\begingroup$ Have a look: "Black Holes in Gödel Universes and $pp$ Waves", arXiv. $\endgroup$ – A.V.S. Mar 9 '18 at 16:54

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