That is, if the closest one we can observe is 1600 light years away, are we not observing these things as they were 1600 years ago? How do we know black holes didn’t just pop up for a brief time window, and now they are gone?
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We have no reason to suspect they magically pop into or out of existence; if they did, we should have seen the effects of them doing so, even if we can’t see the black holes themselves.
Even if you can’t see the black hole, you can observe the effect of the black hole’s gravitational field on spacetime around it.
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