A question that's been bugging me: Why doesnt the gravitational influence of a black hole end abruptly at the event horizon? Supposedly nothing can escape a black hole, so how does gravity itself escape? Light cannot escape a black hole, and gravity travels at the speed of light. Therefore both gravity and light travel below the escape velocity. Thus, gravity cannot escape the black hole. I suppose you could bring up the fact that photons dont interact with other photons, and then extend that to gravity by declaring that gravitons dont interact with other gravitons. But this still leaves something to be desired: how can anything escape the curvature of space-time? If gravitons arent affected by the curvature of space, then what else is there other than space that gravitons can move through? Furthermore, the existence of gravitational waves produced by binary star systems seems to imply to me that gravity does interact with itself. In your explanation, please use math i can understand(no tensors). thanks. Also, another question: How does the inverse square law manifest itself in GR? In newtonian mechanics, its so elegant that the inverse square law is a result of the equation for the surface area of a sphere. And the inverse square law also works for electromagnetism, so im kind of skeptical of general relativity- it just seems to muddle things up. And what happens when division by zero enters the laws of physics?(as in a black hole where distance=0) Does the force become infinite? or is zero distance impossible?
Unlike classical electro-magnetism, GR is non-linear. So if a graviton description of gravity exists (that is still debatable), gravitons should interact with gravitons. As for the "how does the force escape" type questions, I think you are taking the concept of a force mediated by particles too literally. For example, virtual photons CAN escape a blackhole. So if charges fall into the blackhole, from the outside you can indeed tell that the blackhole is charged. Similarly with gravity. Does that help some? It sounds like the main sticking point is the force mediated by particles description, so I'd suggest starting there if you wish to dig further. That usually indicates a failure of the theory (or choice of parameterization). We can't say what happens at the singularity using GR, because GR can't tell us.
As I understand it, to the outside observer the black hole takes an infinite time to form, although in its own frame, the black hole forms right away. In any case, the gravity felt by the outside observer is that of the object becoming a black hole.