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Black holes can emit Hawking radiation. The larger the mass of a black hole the lower the frequency of emitted radiation (aka the temperature of the object). Hawking radiation of a large enough black hole is colder than CMB. In which case the flux of CMB energy onto black hole should exceed the flux of energy from black hole via Hawking radiation. This will increase the mass of a black hole and decrease the temperature of the black hole. It seems that such a black hole has no mechanism to evaporate and must grow larger and larger thanks to the energy of CMB?

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  • $\begingroup$ The CMB is slowly cooling. Be patient! $\endgroup$
    – G. Smith
    Aug 12, 2020 at 20:03

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What you describe is not a stable situation. As the universe expands, the CMB also cools, and that expansion is accelerating. At some point in the future the CMB will cool more than the black hole and it will begin to evaporate.

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