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As photons travel near the event horizon of a black hole they can escape being pulled in by the gravity of a black hole by traveling at a nearly vertical direction known as an exit cone. A photon on the boundary of this cone will not completely escape the gravity of the black hole. Instead it orbits the black hole. These orbits are not stable.

Unfortunately, a black Hole would be unable to "suck in the light rays from our observed galaxy and spit them out again straight back to us" for a couple of reasons.First of all, whilst photon spheres seem to exist......sorry, you cannot view external links. To see them, please REGISTER or LOGINQuoteAs photons travel near the event horizon of a black hole they can escape being pulled in by the gravity of a black hole by traveling at a nearly vertical direction known as an exit cone. A photon on the boundary of this cone will not completely escape the gravity of the black hole. Instead it orbits the black hole. These orbits are not stable....a passing photon will not be traveling "at a nearly vertical direction known as an exit cone", and only photons created close to the Event Horizon of a BH would seem to apply here.Secondly, the path of the photons through space will be curved but for the photons to travel out to the BH and then back to us the path would need to be straight.It's a nice idea though.

A Black Hole is actually the best candidate, as it produces the steepest gravitational gradient and hence the greatest distortion of space-time, which is what you want for gravitational lensing. I seem to recall discussing light being returned to its source via BHs in another recent thread and I think we decided that it might be possible if three+ (but probably not just two) BHs were involved.