# Hawking radiation for closely orbiting black holes

Suppose we have two black holes of radius $R_b$ orbiting at a distance $R_r$. I believe semi-classical approximations describe correctly the case where $R_r$ is much larger than the average black body radiation wavelength due to Hawking radiation.

Do we have approximations for Hawking radiation temperature where the distance $R_r$ is of the same order, or in the case where it is much shorter than the radiation average wavelength?

In the absence of a concrete analysis for either one, Do we have any physical insight to affirm if Hawking radiation will be either inhibited or increased in the above situations?

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I guess the radiation would be inhibited, since the black holes absorb radiation from each other, thus lose mass and hawking-radiate more slowly. –  namehere Dec 8 '12 at 14:27
remember the distance between the BHs is the same order or smaller than the wavelength of the radiation. There might be nontrivial boundary effects that qualitative change the Bogoliubov transformation –  lurscher Dec 8 '12 at 14:40
Just a guess. I'm not bothering to do any serious mathematics so I can't prove anything. –  namehere Dec 8 '12 at 14:42
What exactly do you mean by at a distance $R_r$? –  MBN Dec 8 '12 at 14:55
@MBN Read the first sentence of the question. –  namehere Dec 8 '12 at 14:58