Following on from two recent papers, here we examine the relationship between Newtonian gravitation and general relativity in more depth. This allows us to define a scalar potential which is just the proper time of the vector potential when the latter is interpreted as the geodesic velocity field. The results are closely related to
spacetimes that admit Painlevé–Gullstrand synchronization.
Jaen, J., Molina, A. On the meaning of Painlevé–Gullstrand synchronization. "General relativity and gravitation", 19 Novembre 2015, vol. 47, núm. 12, p. 152-168.