> Einstein’s equations, however, give no prescription for converting the actual, position-dependent, distribution of stress-energy observed at late times into a position-independent source. Croker & Weiner (2019) resolved this averaging ambiguity, showing how the Einstein–Hilbert action gives the necessary relation between the actual distribution of stress- energy and the source for the RW model.
A consequence of this result is that relativistic material, located anywhere, can become cosmologically coupled to the expansion rate. This has implications for singularity-free BH models, such as those with vacuum energy interiors. The stress-energy within BHs like these, and therefore their gravitating mass, can vary in time with the expansion rate. The effect is analogous to the cosmological photon redshift, but generalized to timelike trajectories.
So, yes two different things are presupposed through refined cosmological models:
1) singularity-free black holes limited by vacuum energy and
2) relativistic mass becoming cosmologically coupled to the expansion rate of the universe.
In that case BHs can so-to-speak be "red-shifted" by expanding (empty) space via vacuum-energy and gain mass (> stellar remnant k=3 BHs are the astrophysical origin for the late-time accelerating expansion of the universe.)
One thing to keep in mind, GR as geometrical modeling (field equations) of the universe is at its heart reciprocal. Wheeler[1] captured this succinctly in the now-famous statement: Space-time tells matter how to move; matter tells space-time how to curve.
> Einstein’s equations, however, give no prescription for converting the actual, position-dependent, distribution of stress-energy observed at late times into a position-independent source. Croker & Weiner (2019) resolved this averaging ambiguity, showing how the Einstein–Hilbert action gives the necessary relation between the actual distribution of stress- energy and the source for the RW model. A consequence of this result is that relativistic material, located anywhere, can become cosmologically coupled to the expansion rate. This has implications for singularity-free BH models, such as those with vacuum energy interiors. The stress-energy within BHs like these, and therefore their gravitating mass, can vary in time with the expansion rate. The effect is analogous to the cosmological photon redshift, but generalized to timelike trajectories.
So, yes two different things are presupposed through refined cosmological models: 1) singularity-free black holes limited by vacuum energy and 2) relativistic mass becoming cosmologically coupled to the expansion rate of the universe.
In that case BHs can so-to-speak be "red-shifted" by expanding (empty) space via vacuum-energy and gain mass (> stellar remnant k=3 BHs are the astrophysical origin for the late-time accelerating expansion of the universe.)
One thing to keep in mind, GR as geometrical modeling (field equations) of the universe is at its heart reciprocal. Wheeler[1] captured this succinctly in the now-famous statement: Space-time tells matter how to move; matter tells space-time how to curve.
[0]https://iopscience.iop.org/article/10.3847/2041-8213/acb704/...
[1]https://aapt.scitation.org/doi/abs/10.1119/1.16710?journalCo...