[codethief]

> We aren't falling into a black hole.

I'm going to nitpick here a bit but… we actually don't know. For all we know we could already be inside a gigantic black hole (one that encompasses our entire observable universe). Or our (Earth's) worldline might cross some black hole's event horizon at some point in the far future.

The thing is, the event horizon is not a place in space but a three-dimensional hypersurface that also extends across time. In order to recognize an event horizon you would need to now the entire future evolution of spacetime[0].

[0]: https://en.wikipedia.org/wiki/Absolute_horizon#Nature_of_the...

[eru]

Yes, that might be a valid discussion to be had.

If I wanted to be more precise, I could have said something like 'to a first approximation, we are not currently falling into the black hole in the centre of our galaxy.'

[raattgift]

Yay, I love Big Crunch. BC is such a tasty sugary addictive treat. It generates lots of black holes in the (re-)collapsing universe just like Chocolate Frosted Sugar Bombs generate lots of black holes in Calvin's tooth enamel.

I think I mostly agree with you, loosely, that we could be in a BC cosmos but I also think it's not great science communication to say so because "could" is doing a lot of work there. :-)

Let's start by ignoring the fact that all the new z > 11 (!!!) galaxies JWST is spotting lately do not seem to be rushing inwards from the horizon[*], because I think those observations will kill (inertial) BC dead real soon now.

Expanding R-W gives rise to congruences that are incompatible with collapsing spacetimes, and those congruences are observed (e.g. the timelike geodesic congruence of COMs of galaxy clusters; the CMB's null geodesic congruences; this motivates the use of FRW dusts).

Collapsing R-W is plausible, since the Friedmann equations still work there; collapsing spatially flat FLRW is enough like Oppenheimer-Snyder that it's not worth calling "not a black hole" outside an academic context. I think at best we can say that maybe the expansion reverses at some point, and then try to work out whether evidence strongly disfavours that point being in the past. One would probably start conventionally, trying to measure the critical density by non-geometrical means (since the geometrical approach is pretty suggestive that recently (z < 0.1) parallel lines will stay parallel or diverge). That leaves coming up with some notion of quasilocal mass and counting it, but then I think you're not going to make much progress without a better understanding of the dark sector. Big project, many previous attempts (some high-profile), none especially satisfying.

Now you have me wondering how one deals with the Raychaudhuri vorticity tensor and other terms that would oppose (re-)collapse. Where does all the angular momentum within large galaxy clusters go? Hierarchical BH mergers probably can't be the whole story. I'm not sure we'd worry about that until well into the (re-)collapse, but I think we'd already have to look beyond the FRW dusts. (One would also have to overcome opposition to (re-)collapse from a negative trace of the electrogravitic tensor thanks to a CC-compatible DE. "DE undergoes phase change" is something I'd buy as an idea. Otherwise I think observations from Chandra/ROSAT (data in Vikhlinin et al., 2008) were a fatal problem for BC and big rip).

Ultimately I think we end up in the land of "something about the accelerated expansion would have to give" and speculate wildly against the trend. Taking that path seriously seems like a recipe for frustrating tension headaches.

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[*] the premise here is that BC should look like the actual expansion history under time reversal, and thus we'd expect to find the most distant galaxies brighter, smaller (because we reverse the angular diameter turnaround), and bluer than they are turning out to be.

P.S.: "In order to recognize an event horizon you..." should read Visser 2014 https://arxiv.org/abs/1407.7295

P.P.S.: Yes, "someone" could already have focused shells of radiation on our solar system such that we are already inside an event horizon and don't know it. Somewhere someone diagrammed a Kugelblitz spacetime with that in mind, but I don't seem to be able to find it, and am not sure I trust my memory that it was fairly rigorous (ignoring implausible initial conditions). It wasn't video so it's not the PBS Spacetime "Escape the Kugelblitz Challenge". That's not only very far from rigorous, it's pretty consciously silly. (The challenge should ramp up the mass so that the settled horizon would be trans-Neptunian, and ask whether humanity can engineer anything at all which could escape).

P.P.P.S.: None of this is about falling into an astrophysical black hole like Sag A* as opposed to already unknowingly being in a "black hole".

[codethief]

Thanks for your enlightening comment, raattgift! As always, you know much more about these things than I do, so I won't be able to contribute much to the BC discussion, but I always enjoy learning something new!

The Visser paper I already knew from one of your previous comments. :-)

[raattgift]

Thank you for the kind words.

Nobody's wanted to talk seriously about "terminal" Big Crunch for many years -- the 1998 type Ia SN light curve redshift work that earned the 2011 Nobel prize in physics pretty much killed off the idea of an inertially-expanding universe, rather than an accelerated expansion. It's much easier to recollapse a inertial expansion: "inertial" means there was an effective single impulse that started the bits flying apart from one another, and the bits continue to fly apart along the lines of Newton's First Law. However, as far as anyone can tell the driver of the acceleration is a small positive cosmological constant (constant everywhere in time and space), and to recollapse you have to either turn off (and even reverse) the cosmological constant or you have to overwhelm it with a long-range "fifth force".

This line of discussion surfaces a Big Crunch paper with a wonderful title. In 1982 Andrei Linde proposed his "new inflation"[1] which introduced a scalar field as the driver of inflation. The scalar field starts with high values and slowly rolls down a potential "hill" taking on lower values as it rolls. Part of the hill is very shallow, "sufficiently flat", and so the potential rolls very slowly there; it steepens later. When the evolution of the scalar field is slow compared to the expansion, inflation occurs. When the scalar field is on the steep part, inflation ends. In 2004, Linde and co-authors wrote a paper that used a slow-rolling scalar field to drive the metric expansion (rather than inflation), and in that it is a "fifth force". Rolling slowly near the top of the potential "hill" the scalar field drives the accelerated expansion of space; rolling quickly in the steep part further down the "hill" the accelerated expansion stops and can even reverse leading to an accelerating contraction of space as the scalar field rolls further down an ever-steepening hill and as formerly-separated galaxy clusters become gravitationally bound to one another.

This leads to a relatively quick accelerated shrinking of space, much quicker than the expansion, motivating the poetic title of

Wang, Kratochvil, Linde & Shmakova, "Current observational constraints on cosmic doomsday" (2004, JCAP vol 12).

https://iopscience.iop.org/article/10.1088/1475-7516/2004/12... (aka <https://arxiv.org/abs/astro-ph/0409264>).

Warning, though, that is really a Bayesian reasoning paper dressed up as cosmology. :-) tl;dr: their scheme would destroy the universe in somewhere between 20 billion and 4 trillion years.

There is an assortment papers exploring "big bounce" where there is a partial contraction of the universe; this is often to try to abolish either the singularity at the early boundary or the extremely low entropy at the early boundary. I prefer a Big Crunch that stays crunched, rather than going all soggy and spongey and threatening to cause me to repeat all my mistakes in life over again. Cyclical expansion and contraction also appears with surprising frequency when diverse types of modifications to General Relativity are made, thus it pops up in lots of quantum gravity approaches. These all seem to struggle with observational support for the cosmological constant (and at the extreme anti-de Sitter space has a cosmological constant, but with the wrong sign, which does weeeiiird things, like Hawking radiation reflects off the boundary -- for a single central black hole that means it never evaporates; the same reflecting boundary conditions in an AdS universe with lots of black holes makes the whole universe unstable; and (very) weak vacuum perturbations lead to black holes after sufficiently long times).

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[1] https://www.sciencedirect.com/science/article/abs/pii/037026... (which is also on sci-hub)

[codethief]

Very interesting, thanks so much for elaborating! I was aware of the infamous instability of AdS, but that was about it.

If you don't mind me asking, what is your field of research? (If you like, feel free to share your website or papers or something!) I've read so many interesting comments from you over the past year or two that I've been getting the feeling your interests are quite eclectic. :)