Actually, it is very difficult even for a photon to fall into a black hole, because black holes are very small. So while photons are deflected by its gravity, most of them will miss the event horizon and continue on their merry way.

Gravitons do the same thing: most would just be deflected by the gravity of the black hole, a few would be "eaten" by it.

But the question suggests a possible confusion between real vs. virtual particles. The real photons/real gravitons that are (or aren't) sucked in by the black hole are the ones that form free electromagnetic/gravitational waves. They are quite different from the virtual photons/gravitons that mediate the corresponding interaction.These don't "get stuck". Just as the black hole has a gravitational field, it can also be charged and possess an electrostatic field (the so-called Reissner-Nordström black hole). Just as it interacts with other bodies through the exchange of virtual gravitons, it can also interact with other bodies through the exchange of virtual photons.

But this really is the moment when you should pause for a moment and remind yourself that our best theory of quantum interactions is a field theory. Fields are real: particles are (useful) fiction. Particles are convenient labels that we attach to the terms in the series expansion of an integral that describes an interaction. And in the presence of acceleration or, especially, gravity, the observed particle content is, in fact, observer dependent. That is, different observers have different "natural" forms for that series expansion. So no, particles, be they virtual or real, are not miniature cannonballs that are sucked in by a black hole. The black hole interacts with fields.

It is also useful to remind yourself that, as seen by an outside observer, never mind the singularity, even the horizon is something that has not yet formed. Unless the observer actually crosses that horizon, it forever remains in that observer's infinite future. Which, incidentally, also means that from the outside observer's point of view, all that mass, charge and angular momentum belong to matter that is yet to cross the horizon (which is yet to form). All that matter may have disappeared from sight due to exponential redshift near the (yet to be formed) horizon, and all that matter may already have passed the "surface of last influence", beyond which the outside observer can no longer affect the infalling matter and prevent it from crossing the horizon, but none of that changes the fact that the horizon does not yet exist and nothing crossed it... no material particles, no photons, no gravitons.

@V. T. Toth thanks for your thoughtful and long answer. i truly appreciate the reminders. i hope that you can forgive me for trying to access the hokus pokus that takes place during the collapse of a celestial object to a BH through some physical processes, pretty much as the rest of 'reality' may usually do.

yes, point well taken about virtual particles yet why shouldn't there be gravitons' on the mass shell?  you have a spinning mass isn't it suppose to radiate according to the quadrupole moment? what prevents this radiation (e.g. short wave gravitons) from interfering in a shrinking spacetime? is there a conceptual barrier to comparing between a black body cavity swarming with EM waves to what may happen in a BH? 

call it a BE condensate of gravitons or a soliton can it help us rid ourselves of the singularity?

@Asher: Hmmm, I sense a serious confusion with respect to terminology here. A "graviton on the mass shell" is a just real graviton (i.e., one for which E2 - (pc)2 = 0). This is not to be confused with the event horizon. And yes, a spinning mass would radiate if it has a quadrupole moment, but it also rapidly loses that quadrupole moment in the process (this was, e.g., the "ringdown" part of the GW150914 event).

But the biggest confusion, I think, has to do with your visualization of the black hole as some kind of a "cavity" in three-dimensional space. That it is not. A black hole is where gravity becomes extreme, hence this three-dimensional visualization leads to misunderstandings. For starters, consider: What you think of as the radial coordinate from the outside assumes the role of time inside... and the "center" (i.e., the singularity) is no longer a location in space but rather, a future moment in time.

Whether or not a quantum theory of gravity would help us get rid of the singularity... maybe. But I don't think a naive idea such as simply assuming a condensate would do the trick. For starters, before it makes sense to talk about gravitons even, we need a viable quantum theory of gravity, which we do not have. Also, as I just mentioned, the singularity is now a moment in future time, not a location in space; no clever configuration of a matter field can help you avoid the future.

1) there is a notion of a dynamic horizon

2) the Kerr BH has an ergosphere and an angle dependent radius so a "cavity" is not impossible

3) in a Kerr BH the angular momentum of the mass in the system is the source of the quadrupole radiation -- now if this radiation doesn't escape or dissipates you have a resonator

I think that Lior Liram from Tel-Aviv University will be well equipped to answer this question

there is a certain dilettantism which i apologize for but this is how i learn best.  @Toth here is a quote from Belisky & Verdaguer

"Thus in the stationary axisymmetric case the Kerr and Schwarzschild black hole solutions and their generalizations are soliton solutions."

Belinski, V., and Verdaguer, E.. Cambridge Monographs on Mathematical Physics : Gravitational Solitons. Cambridge, GB: Cambridge University Press, 2001.

Yes: Cf., for example, http://arxiv.org/abs/0801.3805 This is a scattering process, like any other and it has a cross section-that's the quantity that's to be computed. Nothing particularly strange about it, just technique. 

Gravitons or inertons, how do you want to call them and if there is a real need for them, are one-way quanta: from space to inertial poles. So there is no problem them to collapse into the black hole just like photons or any particles.

But the question about the gravitational waves is different because those waves are coming out from gravitational mass poles which changes the gravity field. If event horizons are true and there are massive bodies behind them, the gravitational waves cannot escape. That's why an event horizon seem have to be a flat 2D-plane, wrinkle-free.

We have had thoughts that bodies can fall through an event horizon remaining their structures at least when the black hole is big enough. Should we change this notion?

It's not necessary to focus on cases where individual particles can be resolved-the relevant statement is that gravitational waves can be shown to have a finite absorption probability, in a black hole spacetime, that's all. Just like any other object, nothing different in principle, only the expressions change.

My point is that there seem to be no way for gravitational changes ie gravitational waves to exist and affect outside from a black hole. If  a finite absorption probability wave function is defined only inside an event horizon, only then you can sustain the theory as a consistent doctrine and allow structures behind an event horizon.

No, that's not true: it is possible to define the spacetime (not space!) region that's outside, on and inside the horizon in a coordinate-independent way. And to define the initial and boundary value problems for gravitational wave propagation, that correspond to perturbations of the black hole spacetime and study their evolution and compute their absorption probability, just like any other perturbation of the black hole spacetime.

http://www.sciencefocus.com/article/space/can-gravitational-waves-teach-us-about-inside-black-hole

Stam Nicolis: Is your claim that there are gravitational waves inside in black hole behind an event horizon? ...even that they affect on outside objects/continuum also?

The two spacetimes, outside and inside the black hole horizon are causally separate. But they are usual spacetimes, so they have the expected properties of any spacetime, such as gravitational waves. Of course, those generated inside the black hole don't affect the outside, while those generated outside the black hole do. 

Then, if the gravitational changes cannot escape from a black hole, where are those gravitational vibrations of the lonely black hole from?

https://www.researchgate.net/post/Is_the_gravitational_vibration_after_the_merging_of_supermassive_objects_meaningful

The gravitational waves, that are emitted after a merger of black holes, describe the perturbation of spacetime outside the two black holes initially and outside the result of their merger, finally.

the issue i am trying to press is that independently of any theory of quantum gravity we should be moving to the wavelike aspect of gravity. GR is a geodetic description of spacetime much like optics but spacetime is a medium that generates and mediates waves. it appears to me that wavelike phenomena have the potential to resolve the paradoxes and conundrums associated with focussing geodesics, wormholes and singularities.      

Stam Nicolis: Do you mean that there are still lots of massive gravitational changes outside the lonely black hole result after merger? Based on what?

Based on the gravitational waves detected-the term ``massive'' isn't appropriate here, however: gravitational waves carry energy and momentum, not mass.

I mean gravitational waves are always due to massive changes in gravity field. What is a source when the merger has completed?

When the merger is entirely complete, there are no emissions, you have just the Kerr solution. However, between the time that the hole first make contact and that final state, there is a distortion of the shape, it is those smoothing out of those distortions that produce the rapidly diminishing waves, called the "ringdown phase".