Let me first say Hi to everyone as a new member here! I hope you are all safe, sound, and not too stir-crazy during this Pandemic.
I recently stumbled upon a notion for SETI which seems so simple I was very surprised not to find it in the literature, yet strangely compelling enough that it's given me a new perspective on the Fermi Paradox. I wrote it up here - preprint
Here's a flyover :
For them, a radio signal can cross the Milky Way in 100 years, not 100,000. It is the same for physical exploration at near-light speed. This culture can explore and communicate as if all the space around it has contracted to 1/1000 the size.
OK, now there are a number of ways to achieve that intense time-dilation. Uniform motion very, very close to C is one. A very intense gravitational field is another (so intense it would crush their atoms!)
I did some calculations and could only find one workable possibility : A near orbit around a supermassive black-hole like Sgr A*.
It's in a very peculiar location, between the Photon Sphere and Innermost Stable Circular Orbit. (Such a satellite would be necessarily held in place by artificial orbital corrections.)
At first glance this seems like the most lethal place in the Galaxy to occupy. But the paper shows how radiation, collision with matter inbound from the accretion disk, and so on may be averted (for example, by choosing an orbit that's tilted with respect to the Galactic Plane.)
What I like about this notion is : It offers an explanation as to why ETIs (eager to explore and communicate) haven't been detected : they have migrated to orbit around Sgr A* and are hidden in the radio noise of Sgr A*.
It also suggests a way to try to detect them. That peculiar orbit would have an equally peculiar cyclic doppler shift which could enable us to scan within the noise for it.
In the paper, I calculate what the doppler shift would look like and suggest a means to extract it from the radio noise. (Well, almost. I use the Schwartzchild metric because we don't yet have a good read on the spin of Sgr A* in order to use the Kerr-Newman metric.)
There's another advantage to such a migration to a dilated time-frame. The individual inhabitants now have the option to both speed up as well as slow down their proper time. They can take a trip to a slower time-frame, as anybody can by simply accelerating. But for them there is a new possibility - an excursion to a faster time-frame (any non dilated reference frame)
For example, they could move robots or computers to a conventional time-frame, where their work could be completed at 1000x the rate of their dilated home. Similarly for intellectual labor, their scientists/authors/artists could work in shifts in a conventional time-frame, which would deliver 1000 years of progress annually to their dilated home.
This is admittedly a weird idea. But I would be most grateful if any folks here would like to think about, and very eager to hear your thoughts and criticisms.