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> In the standard black hole model, the collapsing matter that formed the hole hits the singularity and is destroyed Sure, but that's a model for which we don'

> In the standard black hole model, the collapsing matter that formed the hole hits the singularity and is destroyed Sure, but that's a model for which we don't have any observational evidence whatsoever since it's the black hole's interior. That's why I phrased it that way. It doesn't matter, though, even if you say the matter inside the black hole no longer exists (and I'm very happy to entertain that thought): Any sensible definition of mass of the vacuum black hole (i.e. not necessarily the ADM mass since it's defined at infinity but e.g. some definition of quasi-local mass) will still give a non-zero contribution to the mass density.

pdonis 4y ago
> that's a model for which we don't have any observational evidence whatsoever since it's the black hole's interior While this is true, it's not a very strong statement. Physicists extend models all the time into domains where we can't directly test them. The singularity theorems of GR guarantee that the key features of that model, the singularity and the collapsing matter getting destroyed in it, must be true as long as the collapsing matter has the equation of state of ordinary matter. That's why the phase transition I mentioned, to an equation of state corresponding to dark energy, is necessary to avoid forming the singularity and leaving only vacuum in the interior--because the dark energy equation of state violates the energy conditions that are premises of the singularity theorems. > Any sensible definition of mass of the vacuum black hole (i.e. not necessarily the ADM mass since it's defined at infinity but e.g. some definition of quasi-local mass) will still give a non-zero contribution to the mass density. Sure, but this "mass" is not due to the continuing presence of matter somewhere inside the hole. It's a property of the spacetime geometry.
- codethief 4y ago
  > While this is true, it's not a very strong statement. Physicists extend models all the time into domains where we can't directly test them. Sure but it's not every day that we extend models into a domain (near the singularity) where we know our model must eventually break down somehow. So I think you'll see why I'm a bit sceptical about your claim that > the collapsing matter that formed the hole hits the singularity and is destroyed I don't even know what "destroyed" is supposed to mean. Is the claim that the matter simply disappears from the spacetime, with all its conserved quantum numbers and other conserved quantities? As for: > The singularity theorems of GR guarantee that the key features of that model, the singularity and the collapsing matter getting destroyed in it, must be true as long as the collapsing matter has the equation of state of ordinary matter. Do they? The Singularity Theorems assume the existence of a trapped surface. Last I checked[0] (I didn't check deeply, though) the mathematical results on when trapped surfaces arise are very few and far between. Is there a clear proof that in realistic models of black hole formation we must have a trapped surface eventually? [0]: This was in 2020 when the Nobel committee dubiously claimed that Penrose's Singularity Theorems prove that black hole formation and singularities "are a robust prediction of the general theory of relativity".
  - pdonis 4y ago
    > it's not every day that we extend models into a domain (near the singularity) where we know our model must eventually break down somehow Yes, but that doesn't change what the model says. It just affects how likely we think it is that the model is actually realized in our universe. I agree that it's quite likely that the standard black hole model I described isn't realized in our actual universe. But we can still use it if we don't have any better model to replace it with, since even if it breaks down near the singularity, that still leaves the whole rest of the model with plenty of usefulness. What's of great interest about alternate models for collapsed objects that have dark energy inside, like the Bardeen "black hole", is that they do hold out the promise of being a better model to replace the standard black hole model, that doesn't have a singularity anywhere and so would not be expected to break down the way we think the standard black hole model breaks down near the singularity. > Is the claim that the matter simply disappears from the spacetime, with all its conserved quantum numbers and other conserved quantities? The matter disappears, but conserved quantities do not. They remain embedded in the spacetime geometry that is left behind. > The Singularity Theorems assume the existence of a trapped surface. Yes, but the alternate "black hole" models with dark energy inside, such as the Bardeen "black hole", also have trapped surfaces, so this doesn't help to distinguish the models. The singularity theorems also assume energy conditions. Those are the conditions that the models with dark energy inside violate, and which allow those models to not have singularities even though they do have trapped surfaces. > Is there a clear proof that in realistic models of black hole formation we must have a trapped surface eventually? I don't know about "proof", but there are plenty of numerical simulations of realistic collapses of massive objects like stars that show trapped surfaces forming. So I would say it's a robust expectation of any such collapse process, even if we don't have an ironclad proof that it must occur in every single case. > the Nobel committee dubiously claimed that Penrose's Singularity Theorems prove that black hole formation and singularities "are a robust prediction of the general theory of relativity". That statement was justified. But saying that it's a robust prediction if particular conditions are satisfied is not the same as saying that all of those conditions must be satisfied in our actual universe.
    - codethief 4y ago
      > But saying that it's a robust prediction if particular conditions are satisfied But that's not what they said. They said (or implied) it's a robust prediction of GR for our actual universe. > But we can still use it if we don't have any better model to replace it with, since even if it breaks down near the singularity, that still leaves the whole rest of the model with plenty of usefulness. But I never questioned the usefulness of the whole rest of GR? GR is a beautiful and much more satisfying, consistent and mathematically rigorous theory than e.g. QFT, so only because we know its predictions might not hold near singularities I wouldn't dare throwing out the baby with the bathwater. I merely said we don't really know what's happening with the matter once it's inside the black hole / close to the singularity. And it looks like we agree here.

pdonis 4y ago

> that's a model for which we don't have any observational evidence whatsoever since it's the black hole's interior While this is true, it's not a very strong statement. Physicists extend models all the time into domains where we can't directly test them. The singularity theorems of GR guarantee that the key features of that model, the singularity and the collapsing matter getting destroyed in it, must be true as long as the collapsing matter has the equation of state of ordinary matter. That's why the phase transition I mentioned, to an equation of state corresponding to dark energy, is necessary to avoid forming the singularity and leaving only vacuum in the interior--because the dark energy equation of state violates the energy conditions that are premises of the singularity theorems. > Any sensible definition of mass of the vacuum black hole (i.e. not necessarily the ADM mass since it's defined at infinity but e.g. some definition of quasi-local mass) will still give a non-zero contribution to the mass density. Sure, but this "mass" is not due to the continuing presence of matter somewhere inside the hole. It's a property of the spacetime geometry.

codethief 4y ago
> While this is true, it's not a very strong statement. Physicists extend models all the time into domains where we can't directly test them. Sure but it's not every day that we extend models into a domain (near the singularity) where we know our model must eventually break down somehow. So I think you'll see why I'm a bit sceptical about your claim that > the collapsing matter that formed the hole hits the singularity and is destroyed I don't even know what "destroyed" is supposed to mean. Is the claim that the matter simply disappears from the spacetime, with all its conserved quantum numbers and other conserved quantities? As for: > The singularity theorems of GR guarantee that the key features of that model, the singularity and the collapsing matter getting destroyed in it, must be true as long as the collapsing matter has the equation of state of ordinary matter. Do they? The Singularity Theorems assume the existence of a trapped surface. Last I checked[0] (I didn't check deeply, though) the mathematical results on when trapped surfaces arise are very few and far between. Is there a clear proof that in realistic models of black hole formation we must have a trapped surface eventually? [0]: This was in 2020 when the Nobel committee dubiously claimed that Penrose's Singularity Theorems prove that black hole formation and singularities "are a robust prediction of the general theory of relativity".
- pdonis 4y ago
  > it's not every day that we extend models into a domain (near the singularity) where we know our model must eventually break down somehow Yes, but that doesn't change what the model says. It just affects how likely we think it is that the model is actually realized in our universe. I agree that it's quite likely that the standard black hole model I described isn't realized in our actual universe. But we can still use it if we don't have any better model to replace it with, since even if it breaks down near the singularity, that still leaves the whole rest of the model with plenty of usefulness. What's of great interest about alternate models for collapsed objects that have dark energy inside, like the Bardeen "black hole", is that they do hold out the promise of being a better model to replace the standard black hole model, that doesn't have a singularity anywhere and so would not be expected to break down the way we think the standard black hole model breaks down near the singularity. > Is the claim that the matter simply disappears from the spacetime, with all its conserved quantum numbers and other conserved quantities? The matter disappears, but conserved quantities do not. They remain embedded in the spacetime geometry that is left behind. > The Singularity Theorems assume the existence of a trapped surface. Yes, but the alternate "black hole" models with dark energy inside, such as the Bardeen "black hole", also have trapped surfaces, so this doesn't help to distinguish the models. The singularity theorems also assume energy conditions. Those are the conditions that the models with dark energy inside violate, and which allow those models to not have singularities even though they do have trapped surfaces. > Is there a clear proof that in realistic models of black hole formation we must have a trapped surface eventually? I don't know about "proof", but there are plenty of numerical simulations of realistic collapses of massive objects like stars that show trapped surfaces forming. So I would say it's a robust expectation of any such collapse process, even if we don't have an ironclad proof that it must occur in every single case. > the Nobel committee dubiously claimed that Penrose's Singularity Theorems prove that black hole formation and singularities "are a robust prediction of the general theory of relativity". That statement was justified. But saying that it's a robust prediction if particular conditions are satisfied is not the same as saying that all of those conditions must be satisfied in our actual universe.
  - codethief 4y ago
    > But saying that it's a robust prediction if particular conditions are satisfied But that's not what they said. They said (or implied) it's a robust prediction of GR for our actual universe. > But we can still use it if we don't have any better model to replace it with, since even if it breaks down near the singularity, that still leaves the whole rest of the model with plenty of usefulness. But I never questioned the usefulness of the whole rest of GR? GR is a beautiful and much more satisfying, consistent and mathematically rigorous theory than e.g. QFT, so only because we know its predictions might not hold near singularities I wouldn't dare throwing out the baby with the bathwater. I merely said we don't really know what's happening with the matter once it's inside the black hole / close to the singularity. And it looks like we agree here.