[lordfrito]

I very much appreciate your response... you clearly work in this field, and as I said I'm a total layman. So my musings could be utter nonsense.

That said... (bear with me)

> As long as whatever falls in also stays in, the approach is good. But what stops black holes from completely evaporating? In that case, what the hell is supposed to come out of the singularity / deep region / puncture region / excised region?

This is the rub isn't it?

First off, there's a lot of math, and the implications of said math (and GR model), which I'm absolutely not qualified to talk about (and you are). GR makes great (and testable) predictions on the outside of the horizon -- so we have immense confidence in the model, at least as far as we can observe and test.

Singularities in GR present all sorts of problems and paradoxes to us outside of the event horizon (here in the "testable" part of the universe).

I accept that that if we jumped into and found we could probe the interior behind the event horizon of, say, a sufficiently supermassive black hole where tidal forces are small enough we can continue to measure for a little while, then many of the things GR predicts should/would continue to be true. However that's a load bearing if, because it's untestable to an outside whether or not the observer jumping in actually made it inside... GR says that from the jumper's perspective and in their proper time they will cross over, but GR also breaks down in there. We have many reasons to believe the GR model is correct on the outside, but what confidence do we have that a "broken down" GR can be trusted to make predictions on the inside? Maybe things continue as expected, but maybe things don't?

The issue I have is that, from the outside of an event horizon (the rest of the universe), observers can't put together a coherent (and testable) timeline of events for an object falling in that includes a singularity. My understanding is that, due to infinite red-shift, it takes "till the end of time" for any outside observer to see an object cross the horizon. For these observers, the singularity creation event of course take place after the horizon crossing event. If the observer continues to wait for a very long time, they eventually observe the black hole evaporating. This evaporation must occur before the observer sees the object actually cross the horizon, and therefore must occur before the singularity can be said to form. So for all observers on the outside of the horizon, there is never a singularity that exists, or ever exists/existed, or can be interacted with, for all time.

Knowing GR breaks down, who's to say what form the inside of a black hole takes, if there is an "inside" to a black hole at all? The star could collapse into a new form of degenerate matter.. causality could stop... the immense gravity could create a degenerate or infinitely expanding space time where nothing can interact with anything, etc... the point is it's unknowable, and the breakdown of math suggests we're missing something. So we should be skeptical of anything the GR model predicts that's happening on the inside.

So, what I know is that:

   1) I don't have confidence GR predictions of what happens on the inside of the horizon, not just because they're essentially untestable, but especially in light of the fact the GR model breaks down

   2) I do trust the series of GR events that occurs on the outside of the horizon, in the testable part of the universe, which says a singularity makes no sense.

So I have confidence in the belief that in our universe, until the end of time, singularities can't form. Whatever happens "for real" can likely only be explained by a theory that unifies GR and quantum mechanics.

I suspect that whatever the truth behind it is, the answer would tell us a lot about entanglement/entropy, the "speed of causality", and the computational limits of the universe.

I'm a layman, I'm not just not right, I'm not even wrong on most things. Feel free to shoot all of this down!

[raattgift]

Ok, what I take from your comment is that you're identifying General Relativity with certain solutions of GR's Einstein Field Equations. That's like deciding that algebra is just a handful of popular equations.

(Aside, I have run out of time for an editing pass on this comment, so hopefully I didn't leave in ridiculous typos or whatever).

Firstly, let's restrict ourselves to General Relativity as a physical theory. That means we don't have arbitrarily many dimensions with wild metric signatures. We have three spatial and one timelike dimension, so take a metric signature of (+,-,-,-) or (+,+,+,-) which are equivalent but end up with things being written down in different form. That's as opposed to (+,+,+,+,+,+) or (+,+,-,-), all of which can be studied using Einstein's mathematics. Indeed, it's popular particularly among quantum gravity people to work with fewer dimensions (+,+,-) or (+,-) or to go from a Lorentzian (and thus semi-Riemannian) manifold (+,+,+,-) to a Euclidean (Riemannian) one (+,+,+,+). "Quantum gravity people" here include Hawking and 't Hooft. (duck duck go or wikipedia search "Metric signature" for more)

General Relativity as a physical theory of gravitation in our universe 3-spatial-dimension-and-one-time-dimension admits all sorts of really weird spacetimes which are wildly wildy unlike anything in our universe. (In fact relativists have over the decades invented energy conditions in an attempt to remove a few "wildly"s from consideration as possible physical systems: if your spacetime doesn't fulfil some energy conditions everywhere in it, your spacetime is probably not a good match to systems in our universe. For instance, one energy condition requires that energy-density is nowhere negative; another requires that energy is nowhere observed to flow faster than c.) (search term here is "energy condition").

There are a few books worth of exact, analytical solutions to the Einstein Field Equations (those equations define a whole spacetime), some of which resemble astrophysical systems. One such 700-page non-exhaustive book: <https://www.cambridge.org/core/books/exact-solutions-of-eins...>. However there are many many more approximate solutions which have no closed form solution: that's the realm of numerical relativity.

The Schwarzschild black hole spacetime is an example of an exact analytical solution. But there is no superposition of such spacetimes available in General Relativity, so two Schwarzschild black holes in the same universe is not just some linear combination -- instead, we have approximate solutions which can only be solved numerically. That's just with the external properties of black holes: their horizon structures, at least when studying the gravitational waves such systems emit in their last bunch of orbits before merger. It doesn't matter what's inside the horizons for that.

Likewise, where isolated astrophysical black holes give us data is outside the horizon -- what's inside is pretty much irrelevant.

So, the exterior part of an exact solution like Kerr-Newman, with some small perturbations, is at least soluble such that the perturbed KN is an excellent approximation of astrophysical observations of black holes. However we have no observations of the interior part of any black hole, so no way of knowing if Kerr-Newman's interior is wildly unphysical!

(In fact Roy Kerr has said from time to time that because of the presence of matter inside a Kerr BH, the interior part of the solution he arrived at for spinning black holes is probably wrong, even though the exterior part is a remarkably good basis for modelling astrophysical black holes. An example is in his excellent 2016 talk which you can find on youtube at <https://youtu.be/nypav68tq8Q?t=2880> immediately after the 48 minute mark of the video and again at 49:20, however he develops that theme and repeats that point across much of the talk.)

The repair of an unphysical black hole interior might be to stitch together (using a thin-shell method like Darmois-Israel) the physically useful external Kerr solution with something very different inside the horizon but which is more physical. That is not the same, at all, as declaring General Relativity wrong!

Why would one do this? As Kerr implies, there are several invariants ("symmetries") of black hole solutions which are broken by the presence of matter on either side of the horizon. Is the inside part of the Kerr solution fragile to perturbations by matter? That's a work in progress. The outside is pretty clearly stable to such perturbations, mathematically: if you throw in a blob of gas, or star, or shine a very bright light at it, or throw some gravitational waves in its direction, the outside departs from Kerr for a time but soon enough returns to being very well modelled by a Kerr solution with different mass and/or spin. The stability of the inside is not settled. So maybe matter's presence forces a departure from the interior Kerr solution to something else inside, with the Kerr solution remaining in place outside.

Stitching together metrics is something we do all the time. One puts a collapsing patch of spacetime representing a galaxy cluster (in which things tend to move towards the centre, which is where one finds ginormous elliptical galaxies), or a black hole, into a an expanding cosmology (where one finds galaxy clusters flying away from one another) using methods like this. It's all GR, it's just not one single metric line element everywhere.

Of course, there might not be a useful set of metrics that covers the whole of a black hole spacetime, because some region (e.g. near the singularity) demands a theory that differs from General Relativity. For example, the coupling between gravitation and matter might "de-universalize" near the singularity, with some matter moving differently (in particular not falling inwards) compared to matter that moves on GR's trajectories, perhaps because they couple to an auxiliary gravitational field that is so weak away from the centres of black holes that it's never noticed. (This is one approach taken by people who attempt to build relativistic MOND: when gravity is at its weakest, one gets a strengthening of an auxiliary field). [auxiliary here means in addition to the metric tensor, e.g. a vector field on the left hand (curvature) side of the Einstein Field Equations].

However there is no reason from astronomers to prefer alternative theories over General Relativity. The presence of singularities inside black holes might depend on our present toolkit of exact analytical black hole solutions, which are almost all matter-free (vacuum solutions).

Down that line of thinking is confrontation with the work of Penrose and others that shows that singularities are found pretty generically in 3+1d General Relativity. And that's a topic for another time.

[scotty79]

What reason do we have to believe there's anything inside event horizons? Since the matter in dense enough state experiences near infinite time dilation relative to us couldn't it be true that real black holes currently are just very close to becoming theoretical black holes, but will actually never get there? Never as measured by our clocks.