How does gravity escape from black holes?

I know that it is not well established that gravity is made out of gravitons.
I also heard that it is not well established that a graviton is equivalent to a gravitational wave, due to doubt of quantizationability of gravitation.
If gravitons exist, how do they escape a black hole? from its surface as a hawking radiation?
If gravity is only a deformation of space-time, and the volume of its pit in (the fabric of) space-time depends only on the mass within a given volume, then if the event horizon is the surface of a vertical slope of the pit of the black hole, where does it stop from being vertical?
Yes, this question is only about theoretical non rotating black holes.