# Do black holes recapture the CMB?

Basically if I shined a flashlight at a black hole, would I cause it's Hawking radiation temperature increase by more than the temperature of the light I shine at it, at any time during the life of that black hole? Or when CMB photons fall into the black hole are they returned to the universe hotter than the CMB?

Of course you see where I'm going with this. Is there a possibility that black holes counter the heat death?

Adding mass/energy to a black hole doesn't raise but (temporarily) lowers its Hawking temperature.

There's not really a sense of tracking individual photons that fall into a black hole and saying when "those" photons are reemitted. If a black hole starts out colder than the CMB (which all stellar-mass and larger black holes do), then it will cool further as it absorbs CMB radiation. The Hawking radiation that it emits at this stage will be cooler than the CMB. After a really long time, the CMB will be redshifted down to an effective temperature below the black hole's, and only then will the net flow of radiation start exiting the hole and it begins shrinking and heating up. The Hawking radiation that it emits at this stage will be hotter than the CMB.

I don't see how any of this could counter the heat death.

• If larger black holes are colder than the CMB then I don't see how anyone could theorize that the universe was born from a previous universe's big crunch. Jun 7, 2017 at 3:12

No, because black holes themselves eventually evaporate into heat. It's known as Hawking radiation.

An isolated black hole has capture cross-section $$A=\pi (27/4) R_S^2=\pi 27 G^2M^2/c^4$$ and hence absorbs $$P_{in}=\sigma A T_{CMB}^4$$ Watt from the CMB. Meanwhile it emits Hawking radiation with power $$P_{out}=\hbar c^6/15360\pi G^2M^2$$. So the mass changes by $$(P_{in}-P_{out})/c^2$$ per unit of time: $$M' = \left(\frac{ 27\sigma G^2}{c^6}\right ) T_{CMB}^4 M^2 - \left(\frac{\hbar c^4}{15360\pi G^2}\right)M^{-2}.$$

So as long as $$T_{CMB}$$ is greater than the Hawking temperature the hole gains in mass, and afterward it will start losing mass until it evaporates. The background temperature scales as $$T_{CMB}=1/a(t)$$, which if the $$\Lambda$$CDM model is right will approach an exponential decay as $$T_{CMB}(t)=T_{now}e^{-tH_0} + T_{dS}$$ where $$T_{dS}$$ is the horizon temperature ($$\sim 10^{-30}$$ K). This gain is pretty minuscule: over the coming trillion years a million solar mass black hole gains less than $$10^{17}$$ kg of mass from the CMB. So before long (a few trillion years) all holes will start to lose mass unless they are far larger (the size of the cosmological horizon) than expected.

So this process does not stop the heat death. Gravity is working against heat death right now instead: by condensing matter into more tightly bound systems it generates a lot of free energy, and together with energy from fusion processes it can power complex systems.