Can gravitons travel faster than the speed of light? It is common knowledge that not even light can escape black holes, but since the black hole is emitting gravitons, and the gravitons travel in the direction away from the black hole, and it is escaping successfully, are they faster than light?
 A: "Nothing can propagate faster than light" is a condition in GR.
Gravitons are not postulated by GR.
Hence the two (speed limit, and gravitons) are defined by two different theories and it would not be possible to compare things from two different theories unless we are able to combine the two theories, which has not happened yet.
Gravitons, or otherwise - gravity is the one that stops light from escaping the black hole. Same would not apply to gravity. Something like "gravity does not allow gravity to escape black hole", does not make any sense. If gravity stopped gravity to escape black hole, then nothing would experience gravity of a black hole from outside. Which is not true.
It is true that we can not get the information from inside event horizon in the form of light. However, in the form of gravity (or even in form of outer light), we do get the information about motion. A moving black hole tells us that whatever lies behind EH has changed its position in space with respect to other bodies.
Whatever lies behind EH, does influence things outside the EH, via gravity. It does cause change in the curvature of space continuously as it moves along. Something must be making out of the black hole - Something that bars everything else from doing so, and that must be gravity.
Even if gravity crosses the event horizon, it can not be said to travel faster than light.
