Maybe gravity waves propagate at a finite speed. However, they are unlike light in that: light is generated by various reactions and must be generated or it goes out, ceases, whereas gravity is always just there, static, not necessarily propagating at all. Maybe gravity waves are possible, but just an ancillary phenomenon, something that gravity can do but doesn't need to do.
You know, the standard answer to "how do gravitons get out of a black hole?" is that the field is a "fossil" left over from when the hole was a star.
So the obvious question is: if stuff is falling into the hole, how can its gravity increase?
I've seen answers but have a hard time grasping them.
Evidently the integral of the mass/position of the inflow at the moment it crosses the event horizon averages out and the field intensifies that way. I dunno.
--Boris
P.S. Everything radiates EM (light) unless it is at absolute zero...right?