This paper describes black holes as space flowing inward (the rotating hole also twists in a weird way):
http://arxiv.org/abs/gr-qc/0411060
The proper time given by the objects is the same as special relativity except for that fact that they are on a treadmill:
$$ds^2 = dt^2-|v - w|^2$$
where t is "time" in the sense that the (static) geometry is translationally invariant along t, v is the velocity of you, w is the velocity of space. w is a function of the coordinates. The rotating black hole adds a "twist" term that I don't understand well; space itself doesn't rotate!
Is it possible to describe arbitrary spacetimes (i.e. two unequal mass, unequal spin neutron stars colliding to become a black hole) in this fashion? Of course, there may be more than one right answer as you no longer have time translational invariance. What kind of coordinates singularities/caustics would such a description entail?
