Just wondering: why we expect a black hole to have an emissivity of 1? Can anyone give some ideas?
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3$\begingroup$ Do you mean black hole or black body? $\endgroup$– Thomas FritschCommented May 29, 2019 at 14:32
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$\begingroup$ I mean black hole $\endgroup$– CindyCommented May 29, 2019 at 14:42
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$\begingroup$ @ThomasFritsch Why would you assume it is a typo? $\endgroup$– JMacCommented May 29, 2019 at 14:43
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1$\begingroup$ We do not expect a black hole to have an emissivity or absorptivity of 1. “A black hole, being of finite size, is not a perfect black body; the absorption cross section goes down in a complicated, spin-dependent manner as frequency decreases, especially when the wavelength becomes comparable to the size of the event horizon” en.wikipedia.org/wiki/Hawking_radiation $\endgroup$– G. SmithCommented May 29, 2019 at 15:34
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$\begingroup$ @G.Smith So essentially because finite sized black bodies can't exist at all, obviously a BH is not a perfect black body. I'm not sure if that really addresses the spirit of the question, because we could just say nothing real is a perfect black body due to finite size not being able to account for every wavelength. $\endgroup$– JMacCommented May 29, 2019 at 16:00
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1 Answer
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In Classical Thermodynamics emissivity is the same as absorptivity due to the requirement of thermal equilibrium. Since absorptivity is 1, approximately, so is emissivity.
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1$\begingroup$ This is wrong. “A black hole, being of finite size, is not a perfect black body; the absorption cross section goes down in a complicated, spin-dependent manner as frequency decreases, especially when the wavelength becomes comparable to the size of the event horizon.” en.wikipedia.org/wiki/Hawking_radiation $\endgroup$– G. SmithCommented May 29, 2019 at 15:33
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$\begingroup$ Sure, but still it is close to one since the effect is important only for large wavelengths. I have edited the answer to reflect the comment. $\endgroup$ Commented May 29, 2019 at 15:37
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$\begingroup$ Well, at large enough wavelengths, they fall to zero. That is not close to 1! You can’t pretend that long wavelengths don’t matter. The emissivity and absorptivity are highly frequency dependent. $\endgroup$– G. SmithCommented May 29, 2019 at 15:48
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$\begingroup$ We normally don't have wavelengths close to the size of a typical black hole. $\endgroup$ Commented May 29, 2019 at 15:53
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1$\begingroup$ Radio waves have wavelengths up to 100 km. This is much larger than a solar-mass black hole. $\endgroup$– G. SmithCommented May 29, 2019 at 16:06