I think in terms of a combination of the points that Mitch, Robert and Rob have brought up about the fields and virtual particles (Higgs, EM or otherwise). In addition, suppose that there is nothing solid inside the event horizon (except maybe a deep core), and the transition to the interior of the black hole turns everything into light energy (EM field) that is traveling in the virtual form (fields), but perpetually curved back inside so that you get a phased array effect in 3 dimensions of randomized polarity and field strengths so intense that the event horizon becomes an interface that basically 'steers' the direction of all surrounding fields toward the hole. The key question, then, becomes one about inertia. If all of the photons inside have zero inertia/mass, then the randomized curves are possible. If there is any inertia/mass inside, then they would align into a preferred orbit, thus flattening the shape of the event horizon to favor a disc (or the reverse: a dumbell because, reasons). If there are no particles inside, then we get back to the sperical event horizon with an overall sense of 'spin' on the near space caused by the mass of the infalling matter.

Ergo, it isn't the gravitons coming out that cause the effect, but the lack of them (hole theory vs electron flow).