What is so inherently different to the idea of gravitons from other particles, that a black hole draws everything possible including massless photons, but emits gravitons the more the stronger it grows?
If this is something obvious like "^%#^& magnets, how do they work?" please close the question but at least point me to the direction in which should I look.
The photons and gravitons involved in static fields are not causal, they don't propagate along light cones. They are acausal things in a Feynman framework. Any gauge charge is visible outside the black hole, this is because gauge fields are determined by a Gauss law at infinity.
A good classical picture is that a charged black hole has a charge-per-unit-area on the horizon, which is considered as a GR version of an charged plate, the charge per unit area is the electric field density on the horizon, while the horizon always carries mass per unit area away from extremality, and this is by the surface gravity of the black hole.
These classical picture don't refer to particles, only to fields. The duality between particle and field description is subtle, and should not be used for casual arguments like this.
