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It's not that I know too much about it either, I'm just studying it, so got a chain of thoughts in my mind, I still have a long way to go :)
  1. The required unit of chronal potential \phi_t would be \frac{s}{kg \cdot m} If we accept these units for the chronal potential, it means:
Chronal potential is a measure of how time flows per unit of momentum-space displacement.
It inversely scales with mass and position, implying heavier or faster-moving objects dampen the local time flow (sounds heretical to Minkowski and Schwarzschild metrics)
  1. Oh maybe I didn't explain properly, thanks to that, I got caught up in the thought and forgot to define chronal field vector
\vec{C} = -\nabla\phi_t
so it becomes
\Delta t = \vec{C} \cdot |(\vec{T} \times \vec{p})|
so maybe,
\Delta t = \int_{a}^{b} \vec{C}\, \vec{dl}