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There is also no good reason to believe that there is any lower limit on the energy of an individual graviton as there is also no lower limit on the energy of a photon. In fact I expect that assuming the energy is related to plancks constant times the frequency like photons that most gravitons are extremely low energy indeed.
Where do the gravitons originate if not from inside the BH?
Here's a bit of wild speculation about something that ocurred to me concerning photons and BHs that might have some relevance to gravitons and BHs.
Like I said, just a bit of wild speculation.