Is there gravitational black hole radiation? Black holes have entropy and temperature. As Bekenstein and Hawking showed, this yields the emission of electromagnetic radiation in the form of photons: black holes radiate photons. 
The next question is straightforward: do black holes also radiate gravitons? Given that the answer is yes, as the literature shows, what determines the ratio between photon and graviton emission?
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P.S. The question is not about how gravity gets out of a black hole. This is answered in many places. The question is: is there a slow evaporation process of black holes also via gravitons, in addition to the evaporation via photons.
P.P.S. I am not asking about the radiation of massive particles. Only about photons vs. gravitons.
 A: 
Is there gravitational black hole radiation?

The question has two frameworks, the classical General Relativity and the quantum mechanical frame.General realativity has not been definitively quantized, so any answer will depend on future research results.
The assumption is that the gauge boson of the possible quantized gravitation is the graviton, whose coupling constant in feynman diagrams is seen in this table. As you can see it is many orders of magnitude  than the electromagnetic one, and it is coupling constants mainly that set the level of interaction probabilities.
This paper describes the original Hawking calculation for black hole evaporation, I just glanced trough it. It mentions that:

Calculations have also been done for emission of
  fermions and gravitons, linearized perturbations of the metric.

As was  pointed out in  comments the energy for Hawking radiation has to come from the gravitational field, so for any particle production a corresponding vertex with the graviton should exist. For example in this paper  this vertex is described  for graviton photon compton scattering. In the duplicate link, references can be found where calculations have been carried out. Gravitons, in contrast to photons, are self interacting, there exists a three graviton vertex, so a virtual graviton to two gravitons, one virtual and one with a real fourvector that escapes from the horizon, is possible in the strong gravitational field of a black hole.
The answer is that yes there is gravitational radiation coming from the black holes, to a smaller extent than for photons.
