I recently heard somewhere that the cosmic background radiation (CMR, 2.7 kelvin or so) is so much hotter than the "temperature" generated by Hawking radiation of black holes (apparently on the order of a billionth of a kelvin) such that they effectively do not radiate, and are not expected to do so for a loooong time (until expansion of the universe drops the background temp to an incredibly cold temperature).
What I have not been able to determine is when they might be expected to occur? How far in the future will black holes start evaporating? (I believe the answer depends on the size of the black hole as well)
to find the Hawking temperature T_BH of your black hole. Then use the fact that CMB temperature T_CMB is inversely proportional to the cosmological scale factor a(t), where t is time:
Setting this equal to T_BH and solving for t, I get
t = 3.2e16 + ln(2.7 / T_BH) / 2.3e-18 s
So let's say you have a solar mass black hole. Then
T_BH ~ 6.16871e-8 K
and so
t ~ 7.7e18 s ~ 2.4e11 years
i.e. 240 billion years (17 times the current age of the universe).
That's actually not a humongous number, thanks to the exponential expansion of a(t). It would take a lot longer with the expansion rate of a matter-dominated universe (exercise for the reader!)
Some of the larger black holes could take 10^100 years to evaporate even after the universe grows cold. I don’t know how long that would take, but the whole process will take an unimaginably long time.
What I have not been able to determine is when they might be expected to occur? How far in the future will black holes start evaporating? (I believe the answer depends on the size of the black hole as well)