I know that one of the defining features of a black hole is that all matter, including light, cannot escape a black hole. I was wondering if gravitational waves can. If this is true perhaps we could use a form of gravity sonar to map the insides of black holes.
So is it possible for gravitational waves to escape the gravitational pull of a black hole?
The answer to your question is a definite no. Nothing, no particles, no information, can ever escape a black hole.
Electromagnetic radiation cannot escape a black hole, because it travels at the speed of light. Similarly, gravitational radiation cannot escape a black hole either, because it too travels at the speed of light.
How does gravity escape a black hole?
The event horizon is contrary to popular belief, not a physical thing, but a boundary, where the escape velocity equals the speed of light, and inside the horizon it exceeds it. This is the reason why nothing escapes a black hole. In other words, all worldlines inside the event horizon lead to the singularity. This includes the worldlines of the gravitational waves you mention.
