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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

The interesting form of radiation here is not Hawking radiation, but gravitational wave radiation. For astrophysically-sized black holes, the Hawking radiation is completely negligible relative to other processes. For example, for a solar mass sized Schwarzschild black hole, the black hole radiates like a black body at 60 nano Kelvins (far below the background CMB temperature). Certainly the calculation of the Hawking effect in this more complicated setting will be more difficult, but of course the Hawking radiation won't suddenly become important once you have two black holes that are orbiting each other closely.

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