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The capacitor plates idea is beyond my current understanding (no pun intended). I guess it is not possible to polarise the BH and I would assume then that the dielectric constant of the BH is zero - all the effective field lines from the plates would have to bend around the BH making the capacitance lower than would be the case if the BH wasn't there. I will build one in my garden and measure it :-)
I asked him about it, and he sent me this link Graham Black Hole Thermodynamics and Statistical Mechanics by Steve Carlip. I hope it will make it more understandable for us. ==It looks really nice.