Can it be calculated how much light from other stars a black hole of certain sizes would absorb? And how long will it take for the number of active stars to decrease to the point where Hawking radiation would surpass it?
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$\begingroup$ Much ambiguity in that last sentence. What are we measuring the Hawking radiation up to? Average brightness of surrounding stars (in a region of average stellar density) as seen from the black hole? Are we measuring against the stars' emissions, as seen from their atmospheres? What is the mass of the black hole, when does the black hole occur? I don't think your question can be answered unless that's cleared up. $\endgroup$– BMFNov 16, 2019 at 23:22
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$\begingroup$ @BMF I specified in the question that I was talking about black holes "of certain sizes". I'm asking for a range of answers, not in regards to one specific case. $\endgroup$– SnowshardNov 16, 2019 at 23:34
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$\begingroup$ I think that most light will just continue to try to go in a striaght path and curve around it, with a minority touching the event horizon. But right, what's the size of your black hole? Anyway, the longest living stars (red dwarf) have a lifespan of about 10^12 years, whereas the largest blackholes will live for about 10^100 years before evaporating away. $\endgroup$– Louis WaweruNov 16, 2019 at 23:43
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3$\begingroup$ Most of the photons in the universe are in the CMB, not starlight. It will take a long time before the CMB is cooler than the Hawking radiation temperature of even the smallest stellar mass black holes. See en.wikipedia.org/wiki/Timeline_of_the_far_future $\endgroup$– PM 2RingNov 17, 2019 at 9:16
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$\begingroup$ @PM2Ring That is true on average, i.e. in intergalactic space. Inside a galaxy, however, the energy density in starlight will be comparable or bigger than the CMB energy density. $\endgroup$– TimRiasNov 18, 2019 at 10:29
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tldr; extremely little. Space is big, even biggest black holes are ridiculously tiny in physical size
The amount of starlight absorbed by black holes is really minuscule. A black hole is not going to be sucking light in: it can be fairly well approximated to be an absolutely black object around the size of its event horizon (or photon sphere, does not really matter for the purpose for this thought experiment, since photon sphere is 1.5x EH).
Now, let's think of occlusions by more familiar objects: the Moon and the Sun. Now let's think our Moon would be a black hole. Retaining its current size, it would need to have mass in range of about 500 solar masses - pretty big for a BH. It would be also orbiting really close to our Sun; so close, it would probably get eaten by the Moon-BH relatively soon. Also, we would be observing this system really close.
But even in this case, we would still see the Sun most of the time unobstructed. Obstruction means absorption of light, thus there's really not much of this happening.
The amount of absorption of light from a star can be calculated by figuring out the ratio of black hole surface area to the surface area of a sphere with the radius equal to distance between the star and the black hole. In most cases you will be using square kilometers for the BH area, and square light years for the sphere. Which is almost exactly the same as comparing single atom mass to grams.
For the second question, star shine does not really contribute much to the temperature of space, so CMB will dominate this until very very far in the future, when all the stars are already gone
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1$\begingroup$ This answer would be better if it gave an actual number for the absorbed flux per unit of time. $\endgroup$– TimRiasNov 18, 2019 at 10:06
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$\begingroup$ I had to look it up: "In terms of energy flux, the CMB is fairly similar to starlight within our Galaxy.". $\endgroup$ Dec 8, 2019 at 3:27