Hi there,
If you put the Schwarzschild spacetime into a coordinate system in which the time coordinate is identified with the proper time of an observer falling radially from infinity, but keep the other coordinates the same, you get Gullstrand–Painlevé coordinates.
Amazingly, it is...
It is a common theme among background independent quantum gravity theories that there should be some sort of discretization, or fuzziness, of the spacetime manifold occurring on Planckian scales.
It has occurred to me that if we take this discretization to consist of a lattice of sorts, might...