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When the black hole is only detected due to its gravitational effects on other stars and their light, could it be possible that it is in reality a working Dyson sphere?

It would still have at least the mass of the star but also blocks all the emitting light.

I got the idea from watching this Kurzgesagt video about Dyson spheres

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The thing here is that a Dyson Sphere doesn't "block all the emitting light" -- that would violate the conservation of energy. It does absorb the radiation from whatever body it surrounds and then re-radiates it.

As such, it's likely to radiate something like a relatively normal-looking blackbody spectrum, rather than the plasma X-rays from matter falling into a black hole, or the almost-nothing (thus "black") from a black hole with no infall.

As pointed out in @SteveLinton's comment the Dyson sphere would be much larger than the star or a black hole of the same mass in order to not melt, so at that distance the deflection would be far less, since it scales as inverse radius:

$$\approx \frac{m}{r}$$.

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    $\begingroup$ It will also be MUCH bigger than a black hole of the same mass, so any light that passes by it will be only very slightly effected by gravity. $\endgroup$ – Steve Linton Dec 20 '18 at 15:19
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    $\begingroup$ Correct. In fact, the way we'd find a Dyson sphere is by finding a star that shines too dimly for its size. A black hole doesn't shine at all. $\endgroup$ – Nuclear Wang Dec 20 '18 at 15:19
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    $\begingroup$ They could absorb all emitting light, convert as much as they can to electricity, use all the electricity to produce bitcoin (what else?), and dump the waste heat in a direction nobody is looking, while cooling surfaces pointing in the direction of inferior civilisations such as ours down to 2.7K — best stealth space can give? ;-) $\endgroup$ – gerrit Dec 20 '18 at 16:33
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    $\begingroup$ Isn't there a theoretical upper limit on the size of a star that a dyson sphere could encompass too? I'd be doubtful that anything could encompass Canis... $\endgroup$ – Magic Octopus Urn Dec 21 '18 at 13:52

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