Black holes as the source of dark energy

We don't even need an observer to be at infinity, thanks to the expansion of the universe. With some future telescope our descendants may observe something on a trajectory to enter a black hole in an early-universe galaxy that is just crossing that observer's (cosmological) horizon.

I think it's relevant to raise this since the article at the top is about embedding black-hole-like collapsed stars in an expanding universe and the research which directly discusses the observable consequences.

> real physics is local

Yes, absolutely. You still get spaghettified if you fly into a black hole which is the only other appreciable mass left in the far far future of our universe. Nobody needs to see your last moments.

> you have to use the coordinate system of the person falling into the black hole to determine what happens to them

No, you can use any coordinates you want (or no coordinates at all), but you have to be aware that there are quantities which are invariant under changes of coordinates (e.g. the curvature scalars) and quantities which are coordinate-dependent, and that some systems of coordinates make the latter difficult or even impossible to calculate.

Indeed the infaller can use any set of coordinates she or he wants. Some time coordinate (wristwatch? distant pulsars?) and spatial spherical coordinates with the infaller always at the spatial orgin, East-North-Up coordinates originating on the (spinning) black hole, etc. are all (pardon the pun) attractive in these circumstances.

Also, defining exactly where "falling in" happens is tricky, even for the infaller. Visser 2014 on horizons: https://arxiv.org/abs/1407.7295>, second sentence third paragraph of the Introduction section ("These distinctions even make a difference when precisely defining what a "black hole" is -- the usual definition in terms of an event horizon is mathematically clean, leading to many lovely theorems [20], but bears little to no resemblance to anything a physicist could actually measure.")

> better boundary conditions

Ok, what's the curvature scalars about one AU from the one solar mass? How about at about 50 AU (Pluto)? Or about 1000 AU (Sedna)? Or at about 0.8 light years (50 000 AU, in the Oort cloud)?

At what point do we decide that the roughly Schwarzschild metric is no longer useful at predicting the trajectories of things near that central mass? Do we care about the exact contribution of our sun to the invariants in our galaxy's central mass, or Andromeda's? Does a (were-)wolf's baying cause the moon's orbit to change such that it becomes full at a convenient time? The baying does participate in the generation of the 'true' metric, in principle.

[Black holes whose metrics aren't]

> asymptotically flat

means that the scalars drop to the point where we can use a procedure like Israel-Darmois to knit our solar system into the local neighbourhood within the Milky way. Or, if you prefer, that post-Newtonian corrections fall away in the weak field limit. And so we can hierarchically assemble bigger and bigger Schwarzschild or Lemaître-Tolman-Bondi or the like metrics and see that they useful in describing trajectories sufficiently close to the dominant non-relativistically-moving masses, and that Newton's gravitation is a very good approximation at a distance from them.

We do have several lines of evidence supporting this hierarchical approach, e.g the proper motion of galaxies within clusters https://en.wikipedia.org/wiki/Proper_motion>.

[black holes with]

> dark energy inside them

[a] understates the proposed evolution of the non-cosmological-constant energy

[b] conflicts with strong evidence that our solar system is not expanding despite the also strong evidence of the large-scale expansion history of the universe

Roughly, under the contemplated model (thinking generously about how they approach McVittie-like model in light of their paper's §4.6's admission that there is no known solution to the Einstein Field Equations which couples interior vacuum energy, spin, adaptability into the expanding Robertson-Walker metric (like asymptotic flatness gives you), and the evolution from initial formation to growth via accretion)): when approximately a solar mass collapses into a black hole the matter less than a light year from it should expand in a way that does not match the behaviour of the Oort cloud or objects closer in.

In the same section they raise the hope that they can find such a model, and make reference to an existing paper which floated the idea of a gradient and dynamics to the expansion that could be modelled as particualrly relevant around collapsed stars (as opposed to not-yet-collapsed stars of similar mass). This is really deliberately heaping general-relativistic effects in, through, and around an already inherently general-relativistic compact object, followed by hunting for any observational support for that approach (and finding at best weak evidence). It's certainly not KISS.

I just know the basic argument that if black holes are simple, then going from a complex thermodynamic arrangement without a black hole to one with a black hole would represent a spontaneous reduction in entropy. And therefore theories where black holes have a lot of entropy are of interest. While this was originally an argument for string theory, it can be used to argue for other theories as well.

I can't opine on your wild guess that how much hair their model of a not-quite black hole is depends on the embedding. But if it is true, I would expect that embeddings that give it a lot of hair are going to be of more interest than the ones that give it no hair exactly for the thermodynamic reason that I gave.

The formation of a black hole surface around ordinary matter is an increase in entropy if "no hair" is correct. All the individual masses and linear and angular momenta (and electric charge) are hidden behind the trapping surface. By examining that surface you can't tell how many bits and pieces there were inside when it formed initially or which fell in later; only the aggregate values are available. And all of those bits and pieces are crushed into a very small configuration (up to an outright singularity) compared to the volume of the interior. So the interior is mostly vacuum and vacuum is maximum entropy (details for the curious about how this works with a quantum rather than classical vacuum and black hole complementarity: https://arxiv.org/abs/1310.7564v2>).

No-hair might not be correct though. Cf. Hawking's final interests in (https://en.wikipedia.org/wiki/Bondi%E2%80%93Metzner%E2%80%93...>) superrotation and supertranslation "soft" (as in ~zero energy) hair.

> theories where black where black holes have a lot of entropy

Textbook black holes have a lot of entropy.

If "no hair" and a thermal Hawking spectrum up to final evaporation are both correct then low-entropy systems (like a chicken egg or a brain) become hopelessly scrambled and ultimately turned into greybody radiation from which one cannot even in principle determine the antecedent configurations.

That information loss is the upsetting thing, not the balding away of whatever bumps are raised on a black hole as the egg is thrown in balding away in ~ light-crossing time. The then more massive balded black hole (i.e., relaxed back into a "no hair" state) can be entirely represented by a tiny handful of numbers compared to the matter that formed it or fell into it later. Barring something like "soft hair" the numbers required to represent a star like our sun (and an egg) is much much higher than that of an egg thrown into a stellar mass black hole.

That's fine if the egg and all the rest of that stellar mass stays hidden inside the black hole forever. But with Hawking evaporation the shrinking black hole gives us no details of what was thrown in: ultimately, at final evaporation, we would have a stellar mass (and an egg mass) worth of almost entirely photons back. That wrecks unitarity, which is important to particle physicists.

The BMS-group supertranslation and superrotation idea is that the horizon wiggles a bit as the egg is thrown in, and that wiggle emits gravitational radiation with enough complexity in the waves to encode all the microscopic information in the egg (notably lepton number, baryon number, and strangeness).

> black holes have a lot of entropy

So does the infinite empty space surrounding them in a Schwarzschild or Kerr universe. Think like Boltzmann: take a volume of the totally empty space far from a black hole and swap it with a volume of totally empty space somewhere else outside the black hole. Does that make a non-negligible difference to the spacetime? Like, does it light something up, or does it change the geodesic equation? (A: No, not for these vacuum solutions. But it does make a difference if we swap some near-horizon relatively-Hawking-quanta filled space with some emptier far-from-horizon space (n.b., not a vacuum solution).)

Finally, the interior of vacuum-solution black holes (or Lemaître-Tolman-Bondi black holes formed by dust collapse, or other types of dynamical/evolving black holes surrounded by infinite vacuum) is a tiny volume compared to the exterior.

The most relevant volume outside black holes in our universe is the observable volume (set by the cosmic particle horizon), which will not be infinite at times in which there are black holes. There are many ~ billion-solar mass black holes inside the present ~ 10^{80} m^3 observable universe. In the future that volume will be larger, but so will the number of black holes in it, and almost certainly the masses of the largest black holes will be much bigger.

(In the even farther future, if total evaporation happens, there will be no black holes in the big-but-not-infinite observable volume centred on what was our galaxy cluster).