In this paper, Dan Hooper of the Fermi National Accelerator Laboratory proposes that advanced aliens might gather stars from other galaxies as a hedge against the dark energy powered expansion of the universe, to provide starlight to power their civilizations. He doesn't suggest a way to do it; he leaves it up to the aliens to figure out how to build Dyson spheres around stars and harness the energy collected thereby to move the stars. He suggests the possibility of detecting such advanced alien civilizations by the distribution of sizes of stars in galaxies (because only stars in a particular mass range would have long enough lifetimes and low enough masses to move within a useful time).
It's a fanciful and fun idea, but it seems like it might be the least effective way to harness the energy of stars in other galaxies. Wouldn't it be far more efficient for the aliens to use the Dyson spheres to power lasers to direct energy toward their home galaxy? Alternatively, couldn't the aliens power their civilizations (in principle) for a very long time by dropping matter from their own galaxy into the black hole(s) in their galactic center?
I am not asking about engineering methods or choices per se. I'm asking about the physics that might be behind such choices. E.g., can more net energy be delivered from a star over a longer time over intergalactic distances by moving the star, or by putting the star's energy into a laser beam and transmitting the light? And, e.g., how would the energy available within a galaxy via starlight compare with the energy available via dropping matter available in the galaxy into a black hole in the galaxy's center? In the latter case, it seems that some portion of the galaxy's mass would need to be ejected from the galaxy (or the galaxy would need to expand dramatically) in order to send another portion into the galaxy's black hole.