One fun thing think about is that these two galaxies are only aligned from our perspective in the universe. Viewed from a different location, and they're just two normal galaxies.
Also, imagine having the technology to send signals through the lens and get the attention of intelligent life on the other side.
In order to use them as a signaling platform (how?) the signal would have needed to have been sent several billion years ago.
At 10 billion light years away from the most distant lens it is 100% certain that they are no longer in a gravitational lensing configuration.
For a frame of reference, the Milky Way will be in the middle of its epic merger with Andromeda in about 5 billion years.
>In order to use them as a signaling platform (how?) the signal would have needed to have been sent several billion years ago.
Conceivably, a civilization could predict in advance that two galaxies would form a lens configuration, and send a signal that arrived just as the lens formed, correct?
I mostly agree with you. The three body problem (3+) is chaotic at those timescales. But I suppose all thats needed for predicting this lensing is a two body problem if they're isolated enough, which is much more predictable
Take a Monte Carlo approach. Run a bunch of simulations to generate a probabilistic point cloud in spacetime of where the lenses end up. Fire a signal through every point in the cloud.
Which just means there’s no closed form solution. You can simulate these bodies fine provided you have sufficient numerical accuracy and very accurate measurements of initial conditions (this is the part that’s practically impossible)