A vector space is a mathematical paradigm. A more complex vector space is that of Hilbert Space, yet of course they are math metrics rather than space-time in-itself. Time is a meansurement locally of the rate of change of some sort of physical continuum, and obviously with relativity that changes. Scalar fields are a way of assigning a mathematical value- ‘a single number to every point in space’ and thus useful in applied physics. One cannot assign a single value to time with relativity making time values local rather than universal.
I suppose its possible that in a black hole time may experience running in reverse at some point if space-time warps inward upon itself. It is theoretically possible that time runs in different directions at and within an event horizon’s opposing surface directions. Math fields, tensors etc may describe space without in any way explain what the forces are within it. Why it is that galaxies are expanding apparently with space may be reduced or refined with explanations tat are more complete with measurements of particular particles or fields that are increasing spacing externally and if they are not, why it is that just larger clumps of mass have increased spacing. There are new results for the Hubble tension that demonstrate that theoretical astrophysicists aren’t in harmoney even with the rate of expansion. Much to learn obviously.
https://www.space.com/james-webb-space-telescope-hubble-tension-universe-expansion
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