Is there a GR explanation for cosmological coupling causing mass increase as the universe expands? A paper in November 2021 considered the hypothesis that things with mass, including black holes, may be coupled to cosmological expansion so that they slowly gain mass as the universe expands, similar to the coupling that causes light to be redshifted as the universe expands. The paper showed that a simulation of this hypothesis matched well with black hole merger data from gravitational wave observations.
My question is, given that we can explain the cosmological redshift of light pretty well with general relativity, is there a similar explanation, based on general relativity, of how things with mass might gain mass as the universe expands? Or alternately, would it be incompatible with currently-understood general relativity? Or, do we not know either way right now?
 A: This idea is incompatible with general relativity.
In general relativity we know the exact (and unique) solution for a black hole in an accelerating expanding universe. This is known as the Schwarzschild-deSitter (or Kerr-deSitter in the rotating case) solution. These solutions do not exhibit the postulated "cosmological coupling" of the mass.
A: It looks like this paper makes the same mistake as another paper that I discussed in another answer, namely double-counting the matter.
In FLRW solutions, space is filled with perfectly homogenous matter. If you put a black hole in the middle of homogeneous matter, it will eat some of it and grow, and there are even exact solutions to GR that model such situations.
But the homogenous matter is just a smoothed approximation of the matter found in the real world. The growth of black holes by swallowing nearby objects is already accounted for in models of black hole evolution. There is no additional growth due to cosmological matter, because the cosmological matter is the same matter that was already accounted for.
The paper doesn't propose that GR is wrong. The authors assume that GR is correct, not realizing that it rules out their model.
