Hypothetically, could a civilization in a solar system near a supermassive blackhole use the blackhole as a huge gravity lens telescope? I have heard of various proposals that use the massive gravity of stars to sort of focus light at and observe with a suitable telescope placed at such a distance, and I am assuming here that bigger the star in terms of mass, the more focusing and the better images the telescope sees
Assuming a hypothetical civilization, or perhaps humanity developed such a telescope, could they bring it feasibly close enough to a supermassive black hole at the center of say, our galaxy to observe insanely far away celestial bodies and bodies close by with incredible detail?
Typically, uptil what distance could we comfortably resolve details of say, the color and clouds of exoplanets, and view stars with this? A few hundred thousand light years atleast?
It is indeed true that we are contemplating the use of a star: namely, our Sun, as a telescope. The concept is called the Solar Gravitational Lens (SGL). See here for our very latest manuscript, which also contains references to our earlier work: https://arxiv.org/abs/2104.08442
The tremendous light amplification and angular resolution of such a gravitational lens telescope arises from the fact that its light collecting area is effectively the Einstein ring that is seen around the lensing object. The diameter of the Einstein ring determines its angular resolution; its diameter and thickness together determine the light amplification. When using the Sun as a hypothetical telescope, in conjunction with a modest (~1 m aperture) observing telescope, light amplification is of ${\cal O}(10^9)$ and angular resolution is below a nanoarcsecond, though deviations from spherical symmetry in the solar gravitational field tame these numbers somewhat.
These numbers are determined solely by the size of the Einstein ring, i.e., the radius of the Sun (since the Einstein ring has to appear around the Sun; the Sun itself is opaque.) What the mass of the Sun determines is how far away from the Sun images can form. Obviously, the more massive an object is, the more it deflects light, so the sooner light rays can meet. For the Sun, the earliest point where initially parallel light rays passing on opposite sides of the Sun intersect is about 550 astronomical units from the Sun. For a more massive object, this could happen sooner. Or conversely, at a given distance, the Einstein ring seen around a more massive object will have larger radius, corresponding to more light collected and higher angular resolution.
However, the fact that to reach, e.g., Sgr A* at the center of the Milky Way requires travel over several kiloparsecs kind of negates any practical advantage that an SMBH might offer as a practical gravitational lens telescope. Any civilization possessing the technology to travel across the Milky Way (assuming such technology even exists within the realm of physics) probably has other, more practical means at their disposal to make astronomical observations of the deep sky.