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As a complement of this Phys.SE question.

What kind of lensing and diffractions effects from space would be perceived on earth?

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    $\begingroup$ It would be so small, you could only see its effects in a telescope. However, conceptually, take a small lens, black out its center with a permanent marker, and hold the lens at the arm length against the night sky. $\endgroup$ – safesphere Jun 5 '18 at 16:35
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The Schwarzschild radius of a solar mass black hole is about a kilometre, so the event horizon would be too small to see (even if it had been luminious) at 1 AU distance. The visual distortions around a black hole also extend a few radii out, so if we generously say the whole system is 10 km across the angular diameter is about $6.7\times 10^{-8}$ radians, or 0.014 arcseconds. This is smaller than the angular diameter of many stars in the sky.

It would likely produce lensing that would be fairly detectable in a small telescope, and since Earth moves there would be frequent lensing events that might be noticeable with the bare eye if one were lucky to see it amplify a bright star.

Now, if the black hole had an accretion disk it would be very noticeable. The disk size itself would potentially be small but likely enough to make it look disk-like: white dwarf novas range from 10 km to $10^5$ km, X-ray binaries 10 km to $10^6$ km. It would be very bright, emitting light mostly in the X-ray spectrum but of course also many times more than the sun in the visible spectrum. The light would be pretty actinic in colour due to the short-wavelength dominance.

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As a complement to the already good answer by Anders Sandberg. Some further consequences of the sun being a black hole (presumably of the same mass):

  • Since a black hole does not emit any radiation, it would be night permenantly.
  • Because there is no light from the Sun to illuminate objects in the solar system. The moon would be dark disk mainly visible due to it blocking starlight. We probably would not be able to see the other planets at all.
  • Because the atmosphere is not being heated by the Sun, it would be much cooler. One of the consequences (for the night sky) would be that stars twinkle less.
  • As already noted the angular size of the black hole on the Sky would be very small. I think it is worth noting that the gravitational field outside the normal radius of the Sun, would be almost identical to the field produced by the Sun. Hence outside the angular size of Sun, the night sky would like almost exactly like what we currently observe during a solar eclipse.
  • If you would point a telescope at the black hole it would look something like this: from (SXS collaboration?): https://3iom3142cnb81rlnt6w4mtlr-wpengine.netdna-ssl.com/wp-content/uploads/2018/04/fig1-1.png
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