Suppose we have two black holes of radius Rb orbiting at a distance Rr. I believ

Question

Suppose we have two black holes of radius Rb orbiting at a distance Rr. I believe semi-classical approximations describe correctly the case where Rr 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 Rr 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?

Explanation / Answer

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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