There are several things to it. One is the definition of pair production at the event horizon. In it we read 'anti particles' are what falls in, annihilating as they meet 'particles'. Assuming the possibility of there being 'particles' falling in you get a addition as you so rightly point out. I seem to remember a discussion we had about this here, with a guy explaining the concept behind why all 'particles' passing the event horizon by necessity becomes 'anti particles', but I can't seem to find it?

I've seen a definition though in where it's the 'energy' it cost to create and separate those particles in the Black Holes gravitational field that will make the Black Hole lose mass. Looking at it that way you may be able to account for the addition of energy inside the EH (Event Horizon) as the annihilation takes place too, maybe? Because, even if annihilating it still will leave a excess of 'energy' inside that EH, as I think of it?

Maybe the last one can be ignored if we assume the 'energy' to be something that pass the EH, much like gravity does? But the radiation released can't leave though, it all goes back to what 'energy' means to me. (the question there is what it cost to 'transform' and if the 'heat' released is equivalent to the cost? If it is so then 'energy' is transformations and the conservation laws is upheld. In the other case, if 'something more' is lost?)

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Thinking of it, assuming that this is a correct definition, the amount of particles or anti particles infalling shouldn't matter for it. You can always use statistics and define a proportionality to the amount, and doing so that proportionality must still be less, than the 'energy' stolen from the Black Holes Event Horizon (4 big letters in a row

as the pair production happen. Anyway, it imply that the cost for creating is bigger, for the BH gravitational field, than the energy/heat/radiation added through what is annihilated inside. Which should be correct considering that proximately half of the particles gets added to our side of the universe, the other half either adding, or getting destroyed releasing 'energy', inside that Even Horizon.

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Rereading I better point out that 'gravity' is a geometry in relativity, not any 'energy' per se, although you have gravitational waves taking with it 'energy', as (possibly) proven by binary stars losing energy due to gravitational waves propagating from them as they rotate around each other. We know that all energy adapt to gravitation though so there must be a close relation between them anyway.