My understanding of a global time function is this: a function whose value always increases as a body moves into its local future.

My confusion is this: I gather that the Gödel Universe is bizarre because no such function is definable (due to closed timelike curves). But doesn't relativity of simultaneity in our universe also mean that no global time function can be defined?

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    $\begingroup$ No, it only means that this function is not unique. Freedom of choice of a time function is related to freedom of choice of foliation by Cauchy hypersurfaces, via $T^{-1}(t) = \Sigma_t$ $\endgroup$ – Slereah Feb 20 '18 at 22:48
  • $\begingroup$ Many cosmological models have a preferred time coordinate, whose gradient is, for example, parallel to the Hubble flow or to the gradient of the temperature. That doesn't mean they're preferred by the laws of physics. $\endgroup$ – Ben Crowell Feb 20 '18 at 23:35
  • $\begingroup$ @daisy - This webpage explains relatively simply with a video the shape of the spacetime as one moves through it: iopscience.iop.org/article/10.1088/1367-2630/15/1/013063 -- Also see: itp1.uni-stuttgart.de/institut/arbeitsgruppen/wunner/… for more info. It's not indefinable, it simply wraps in certain directions. $\endgroup$ – Rob Feb 21 '18 at 1:37
  • $\begingroup$ Not only does our universe have a global time function but there is a privileged one extensively used in cosmology, so called cosmic time. The "age of the universe" from Big Bang to now is given in cosmic time, see Can the universe have different ages? $\endgroup$ – Conifold Feb 21 '18 at 3:56

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