Black Holes - the two points of view.

[PAllen]

Are you saying that having test particles enclosing the singularity implies there's no vacuum?
But the singularity is at the center and the spacetime is foliated by 2-spheres that *enclose* the singularity so how could they not enclose it?

Actually, a free-falling initially locally spherical cluster of test bodies can never enclose the singularity. The definition of this procedure is that you start with a small enough ball of 'dust' that in some spatial slice it is geometrically arbitrarily close to a Euclidean 3-ball, then watch how it changes over a short period of time along the world lines. No such ball enclosing the singularity can ever have the geometry of a 3-ball. Further, the singularity is not even considered part of the manifold, so an alleged 3-ball enclosing it would not be a connected set.

 

[PAllen]

I meant that a time-invariant and time-symmetric system in a circular orbit behaves as if time is constant, that's why they are called static.

Can you clarify what you mean? This makes no sense to me. A circular orbit world line advances steadily in proper time and in SC coordinate time. It is a helix in SC coordinates.

What Peter is saying is that a curve of constant (r,theta,phi) with t varying is not a geodesic - it has proper acceleration. A curve of constant (t,theta,phi) with varying r is also not a spacelike geodesic. Do you disagree with either of these statements?

 

[PeterDonis]

I meant that a time-invariant and time-symmetric system in a circular orbit behaves as if time is constant, that's why they are called static.

I have no idea what this means, but whatever it means, it doesn't show that the worldline of an object in a free-fall orbit is an integral curve of any KVF, which was my point.

 

[PeterDonis]

Are you saying that having test particles enclosing the singularity implies there's no vacuum?

No vacuum somewhere inside the sphere, yes; in this case, no vacuum at the singularity at r = 0. But there is still vacuum everywhere else.

But the singularity is at the center and the spacetime is foliated by 2-spheres that *enclose* the singularity so how could they not enclose it?

You're confusing your spheres. The "spheres" referred to in the Baez web page you linked to are spheres of test particles; they can be anywhere you like, enclosing the singularity or not. The 2-spheres that foliate the spacetime according to its spherical symmetry enclose the singularity, yes, but those 2-spheres aren't the ones Baez is talking about.

[Edit: See my following post in response to PAllen; I was thinking of 2-spheres in the above, but I think PAllen is correct that Baez' actual argument refers to 3-balls, meaning 2-spheres plus their interiors. In that case a "sphere" enclosing the singularity doesn't meet Baez' specifications to begin with, so I was wrong to bring it up as a possible example.]

 

[PeterDonis]

Actually, a free-falling initially locally spherical cluster of test bodies can never enclose the singularity. The definition of this procedure is that you start with a small enough ball of 'dust' that in some spatial slice it is geometrically arbitrarily close to a Euclidean 3-ball, then watch how it changes over a short period of time along the world lines. No such ball enclosing the singularity can ever have the geometry of a 3-ball.

Hmm. I was thinking of the "sphere" as a 2-sphere of test particles, the 2-sphere that marks the boundary of a 3-ball, not the 3-ball itself. But re-reading the Baez web page, I think you're right, he means for it to be the full 3-ball, including its interior as well as its boundary. In that case, yes, you're right, no ball of test particles that encloses the singularity can meet his specifications.

Further, the singularity is not even considered part of the manifold, so an alleged 3-ball enclosing it would not be a connected set.

Yes, if the interior of the 3-ball has to be included as well as the boundary, you're right. The boundary itself, the 2-sphere, can still be a connected set, but its interior cannot.

 

[Dale]

What Peter is saying is that a curve of constant (r,theta,phi) with t varying is not a geodesic - it has proper acceleration. A curve of constant (t,theta,phi) with varying r is also not a spacelike geodesic. Do you disagree with either of these statements?

I agree with the first, but I question the second. Although I haven't solved the geodesic equation to prove it I think that the second would have to be a geodesic by symmetry.

 

[PeterDonis]

What Peter is saying is that a curve of constant (r,theta,phi) with t varying is not a geodesic - it has proper acceleration. A curve of constant (t,theta,phi) with varying r is also not a spacelike geodesic.

Those two statements are both true, but they're actually not what I was saying. What I was saying was that a curve of constant (t, r) but varying (theta, phi) cannot be a spacelike geodesic. Since any integral curve of one of the 3 KVFs arising from spherical symmetry must have constant (t, r) and varying (theta, phi), it follows that no integral curve of one of those KVFs can be a spacelike geodesic (contrary to what stevendaryl had said in the post I was responding to). The worldline of an object in a free-fall orbit can be a (timelike) geodesic, but such a worldline will not have constant t, only constant r (and of course it will have varying theta, phi), and it will not be the integral curve of any KVF.

 

[PAllen]

I agree with the first, but I question the second. Although I haven't solved the geodesic equation to prove it I think that the second would have to be a geodesic by symmetry.

Oops, you are right (I just did work out the geodesic equations). I had blithely assumed that since radial spacelike geodesics 4-orthogonal to various free-fallers are r as f(t), that that covered all radial spacelike geodesics. So: constant (t,theta,phi) varying r is a spacelike geodesic, and definitely satisfies the geodesic equation with a suitably chosen affine parameter (that obviously cannot be t).

[above analysis only done for exterior region].

 

[PeterDonis]

constant (t,theta,phi) varying r is a spacelike geodesic

Hmm, yes, I missed this one.

[above analysis only done for exterior region].

The geodesic equation is the same in the interior region, so constant (t, theta, phi) varying r should still be a geodesic there--a timelike one instead of a spacelike one.

 

[Dale]

Oops, you are right (I just did work out the geodesic equations).

Thanks for doing that! That is helpful.

 

[Dale]

This got lost in the debate. My question was trying to clarify how in the non-static(in this case contracting) metric inside the EH can we have a vanishing Ricci curvature when Ricci curvature describes (according to Baez at least:http://math.ucr.edu/home/baez/gr/ricci.weyl.html) change of volume, I though one of the hallmarks of expanding or contracting spaces was precisely change of volume.

I don't think that the Schwarzschild spacetime is contracting inside the EH. Is that just an assumption, or do you have a reference or a calculation that supports that?

Also, I am kind of lost as to the purpose of the recent lines of discussion. We seem to agree that the interior of a black hole has a spacelike KVF, is therefore not static, and yet is vacuum. We also seem to agree that Birkhoff's theorem, properly stated, avoids claiming otherwise. We seem to agree that the standard Schwarzschild coordinates may not be the best ones to use inside the EH. So what remains? I see that something still bothers you, but the objections you are bringing up recently seem like just throwing out random concepts unrelated to any of the previous discussion.

 

[TrickyDicky]

Can you clarify what you mean? This makes no sense to me. A circular orbit world line advances steadily in proper time and in SC coordinate time. It is a helix in SC coordinates.

What Peter is saying is that a curve of constant (r,theta,phi) with t varying is not a geodesic - it has proper acceleration. A curve of constant (t,theta,phi) with varying r is also not a spacelike geodesic. Do you disagree with either of these statements?

Hmmm, do you agree that in Schwarzschild solution there are circular orbits(stable only up to 6GM and unstable from 6 to 3GM). These are usually considered geodesics, right? And according to stevendaryl having constant r, theta, phi they correspond to integral curves of timelike KVFs.

 

[Dale]

Hmmm, do you agree that in Schwarzschild solution there are circular orbits(stable only up to 6GM and unstable from 6 to 3GM). These are usually considered geodesics, right? And according to stevendaryl having constant r, theta, phi they correspond to integral curves of timelike KVFs.

A circular orbit is a geodesic and it does have constant r and theta, but phi and t vary. They are not integral curves of any KVF.

I really don't understand this desire to link geodesics with KVFs. They are unrelated. I guess this is the part that seems random to me. I just don't get it at all.

 

[TrickyDicky]

I don't think that the Schwarzschild spacetime is contracting inside the EH. Is that just an assumption, or do you have a reference or a calculation that supports that?

It is just the educated guess that all 4-spacetimes that are not stationary(not including the cosmological constant in the EFE) must have an either expanding or contracting 3-space volume. But maybe this is not the case here.

Also, I am kind of lost as to the purpose of the recent lines of discussion. We seem to agree that the interior of a black hole has a spacelike KVF, is therefore not static, and yet is vacuum. We also seem to agree that Birkhoff's theorem, properly stated, avoids claiming otherwise. We seem to agree that the standard Schwarzschild coordinates may not be the best ones to use inside the EH. So what remains? I see that something still bothers you, but the objections you are bringing up recently seem like just throwing out random concepts unrelated to any of the previous discussion.

I'm trying to tie up all the (for me) loose ends. That's all.

 

[PeterDonis]

Hmmm, do you agree that in Schwarzschild solution there are circular orbits(stable only up to 6GM and unstable from 6 to 3GM). These are usually considered geodesics, right?

Yes.

And according to stevendaryl having constant r, theta, phi they correspond to integral curves of timelike KVFs.

That post by stevendaryl was in error. See the whole series of recent posts from me, PAllen, and DaleSpam on that subject.

 

[Dale]

I'm trying to tie up all the (for me) loose ends. That's all.

OK, but if it isn't too much hassle, I would appreciate if you could explain how any remaining loose ends connect back to the rest. Especially the KVF->geodesic connection.

 

[PAllen]

I think the idea of contracting space in the SC interior comes from the waterfall analogy. You can view the dynamics (loosely) as spacetime collapsing and being consumed at the singularity - and being created at the horizon. A key point is that there are always a complete sequence of 2-spheres for all area defined radii > 0 and < Rs, shown most easily using Lemaitre coordinates. Thus, the volume inside the EH remains constant.

Similarly, as Peter described in an earlier post, a ball of free falling dust maintains its volume (while getting stretched and squeezed), up to the singularity.

The SC singularity is described in the literature as a Weyl singularity, while that in FRW collapse is a Ricci singularity. And here, my knowledge stops - I do not claim to know the technicalities of what is the difference between a Weyl singularity and a Ricci singularity.

 

[PeterDonis]

It is just the educated guess that all 4-spacetimes that are not stationary (not including the cosmological constant in the EFE) must have an either expanding or contracting 3-space volume. But maybe this is not the case here.

It depends on how you slice the spacetime (or the region of spacetime, such as the region inside the EH) into 3-spaces. There are ways to slice the region inside the EH into 3-spaces such that the 3-volume of all the 3-spaces is constant; for example, use slices of constant Painleve "time" T. I put "time" in quotes because inside the EH the Painleve T coordinate is spacelike, even though surfaces of constant T are *also* spacelike.

However, I believe that the following statement, which may be what is underlying your educated guess here, is correct: given any family of *timelike* geodesics that covers the entire region inside the EH, the family of spacelike surfaces orthogonal to those timelike geodesics will be decreasing in volume as proper time increases along the geodesics. In this sense, you could say that space inside the EH is "contracting". However, that statement does not have all the same implications as it would in, for example, FRW spacetime.

 

[PeterDonis]

The SC singularity is described in the literature as a Weyl singularity, while that in FRW collapse is a Ricci singularity. And here, my knowledge stops - I do not claim to know the technicalities of what is the difference between a Weyl singularity and a Ricci singularity.

As I understand it, a Weyl singularity has the Weyl tensor components going to infinity, while a Ricci singularity has the Ricci tensor components going to infinity. In the cases you name, the other tensor (Ricci for the Weyl singularity, Weyl for the Ricci singularity) is zero (in the idealized case), so *all* of the curvature is described by the tensor that goes to infinity at the singularity.

 

[PeterDonis]

However, I believe that the following statement, which may be what is underlying your educated guess here, is correct: given any family of *timelike* geodesics that covers the entire region inside the EH, the family of spacelike surfaces orthogonal to those timelike geodesics will be decreasing in volume as proper time increases along the geodesics.

On thinking it over some more, I'm no longer convinced that even this statement is true, because the worldlines of ingoing "Painleve observers" are timelike geodesics, *and* they are orthogonal to each surface of constant Painleve "time" T that they pass through, and as I said, each surface of constant T has the same 3-volume inside the horizon. So the infalling Painleve observers do *not* see a decreasing 3-volume of the "spaces" they pass through.

In fact, thinking it over still more, I'm not even convinced that the statement as I gave it is true for observers falling in along a geodesic of constant Schwarzschild t inside the EH. Such observers do pass through 2-spheres of decreasing area; however, the 3-volume of each 3-space orthogonal to their worldline, which is just a 3-surface of constant r < 2m, is *infinite* (one 2-sphere at r for each value of t, with a fixed finite area of 4 pi r^2, but the 3-surface as a whole covers the full infinite range of t, so its total 3-volume is infinite).

So I think the only sense in which space can be said to be "contracting" inside the EH is that any timelike observer must pass through 2-spheres of strictly decreasing area.

 

[TrickyDicky]

OK, but if it isn't too much hassle, I would appreciate if you could explain how any remaining loose ends connect back to the rest. Especially the KVF->geodesic connection.

As I said I forgot why I brought it up in the first place, then I came back to it from a stevendaryl's post I had not spotted previously. I agree that it is not related to what we are discussing and I won't mention it here again. It might make a good question for the Topology and geometry subforum though.

 

[TrickyDicky]

It depends on how you slice the spacetime (or the region of spacetime, such as the region inside the EH) into 3-spaces. There are ways to slice the region inside the EH into 3-spaces such that the 3-volume of all the 3-spaces is constant; for example, use slices of constant Painleve "time" T. I put "time" in quotes because inside the EH the Painleve T coordinate is spacelike, even though surfaces of constant T are *also* spacelike.
However, I believe that the following statement, which may be what is underlying your educated guess here, is correct: given any family of *timelike* geodesics that covers the entire region inside the EH, the family of spacelike surfaces orthogonal to those timelike geodesics will be decreasing in volume as proper time increases along the geodesics. In this sense, you could say that space inside the EH is "contracting". However, that statement does not have all the same implications as it would in, for example, FRW spacetime.

I see what you mean about the dependence on the slicing, and dealing with GR manifolds there should not be preferred slicing. So the slicing in which the 3-volumes are constant shouldn't be preferred over the "contracting" one or viceversa. See also that this can classify our coordinate patches in static and not static ones:look for instance to the example of de Sitter space where you can choose between static or non-static coordinates.
However, maybe you can also see that there is a certain ambiguity about this wrt 4-spacetimes in GR. In the sense that in order to decide whether a spacetime, or at least a patch of the spacetime is static or not we must "choose" a preferred way of slicing it into 3-spaces, in other words one must choose a preferred frame.
This can be clearly seen in FRW metric, being a GR spacetime we are in theory allowed to slice it whichever way we want, no preferred frame, however in practice there is only a slicing that allows us to consider it an expanding "space", the one with slices of homogeneous density. Other slicings may give us expanding "spacetimes" which make expansion lose its original meaning.
I guess when you say this situation cannot be compared with the Black hole inside because in this last case we are not demanding homogeneity(after all it is supposed to be a vacuum), you might be right. But as I said, as long as this interior is modeled as an S^2XR^2 space in which every point is a 2-sphere you have homogeneity, and given the finite volume inside the EH and that it might be full of matter that has fallen in the BH on its way to the singularity,I find it hard not to think of this inside region as one where the comparison with the FRW metric is valid to a certain extent.

On thinking it over some more, I'm no longer convinced that even this statement is true, because the worldlines of ingoing "Painleve observers" are timelike geodesics, *and* they are orthogonal to each surface of constant Painleve "time" T that they pass through, and as I said, each surface of constant T has the same 3-volume inside the horizon. So the infalling Painleve observers do *not* see a decreasing 3-volume of the "spaces" they pass through.

In fact, thinking it over still more, I'm not even convinced that the statement as I gave it is true for observers falling in along a geodesic of constant Schwarzschild t inside the EH. Such observers do pass through 2-spheres of decreasing area; however, the 3-volume of each 3-space orthogonal to their worldline, which is just a 3-surface of constant r < 2m, is *infinite* (one 2-sphere at r for each value of t, with a fixed finite area of 4 pi r^2, but the 3-surface as a whole covers the full infinite range of t, so its total 3-volume is infinite).

So I think the only sense in which space can be said to be "contracting" inside the EH is that any timelike observer must pass through 2-spheres of strictly decreasing area.

See my comments above.
There is something I can't fully understand about this dependence of spacetimes on the frame or the coordinate patch chosen to decide about their staticity or lack of it, when it is supposed to be something invariant and as you and other have insisted the KVFs shouldn't depend on the coordinates.
I know at least in Riemannian geometry KVFs are defined globally so in a space there cannot exist regions with different KVFs,that assures that they are truly coordinate independent entities, but then again in those spaces there is no timelike-null-spacelike distinction.
But in pseudoriemannian spacetimes I'm not sure this holds as simply as that. At least my discussion above suggests that there may be a dependence on the slicing, that is on the frame and coordinates chosen to have a KVF being timelike or spacelike.

 

[TrickyDicky]

I think the idea of contracting space in the SC interior comes from the waterfall analogy. You can view the dynamics (loosely) as spacetime collapsing and being consumed at the singularity - and being created at the horizon. A key point is that there are always a complete sequence of 2-spheres for all area defined radii > 0 and < Rs, shown most easily using Lemaitre coordinates. Thus, the volume inside the EH remains constant.

Similarly, as Peter described in an earlier post, a ball of free falling dust maintains its volume (while getting stretched and squeezed), up to the singularity.

Actually the waterfall image with the eternal spring and sink that mantains the volume in a time-invariant way has its beauty and is inspiring, but doesn't it look like a completely static image of a spacetime to you?
There's something of a catch-22 situation with the geometry of this region, it would seem to admit either a timelike or a spacelike KVF depending on the slicing in a kind of situation that reminds of the de Sitter space static and expanding coordinate patches.
See my reply to PeterDonis in my previous post.
Going back to the waterfall analogy and to reinforce the sometimes slippery distiction between static and non-static that I see in the inside region of a BH, consider this statement from the wikipedia page "spacetime symmetries" where it consideres Einsten static spacetime as a subcase of FRW metrics:
"For example, the Schwarzschild solution has a Killing algebra of dimension 4 (3 spatial rotational vector fields and a time translation), whereas the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric (excluding the Einstein static subcase) has a Killing algebra of dimension 6 (3 translations and 3 rotations). The Einstein static metric has a Killing algebra of dimension 7 (the previous 6 plus a time translation). "

This is made clearer here, from the wikipedia page on de Sitter universe, where the Einstein static spacetime is made a special case of de Sitter spacetime (that is considered here as a FRW metric without privileged frame so that it is an expandig "spacetime" rather than "space" in accordance with the perfect cosmological principle) in a similar way to the waterfall description in which as you say the dynamics of collapsing at the singularity and "creation" at the EH are finely tuned too to produce a static volume:
"As a class of models with different values of the Hubble constant, the static universe that Einstein developed, and for which he invented the cosmological constant, can be considered a special case of the de Sitter universe where the expansion is finely tuned to just cancel out the collapse associated with the positive curvature associated with a non-zero matter density. "

 

[PeterDonis]

Iin order to decide whether a spacetime, or at least a patch of the spacetime is static or not we must "choose" a preferred way of slicing it into 3-spaces, in other words one must choose a preferred frame.

Not for the standard definition of "static", which is that the spacetime (or a region of it) has a timelike KVF. That definition is coordinate-independent. By that definition, Schwarzschild spacetime (the vacuum solution) is static only outside the EH; the region at and inside the EH is not static.

This can be clearly seen in FRW metric, being a GR spacetime we are in theory allowed to slice it whichever way we want, no preferred frame, however in practice there is only a slicing that allows us to consider it an expanding "space", the one with slices of homogeneous density. Other slicings may give us expanding "spacetimes" which make expansion lose its original meaning.

There is also a coordinate-independent definition of "expansion", but it applies to families of timelike curves, not "space" itself. The standard definition of an "expanding" or "contracting" FRW spacetime uses the family of timelike curves that describe the worldlines of "comoving" observers; the expansion of that family of curves, defined in the standard coordinate-independent way, is positive for an expanding FRW spacetime and negative for a contracting one.

But as I said, as long as this interior is modeled as an S^2XR^2 space in which every point is a 2-sphere you have homogeneity

Not by the standard definition of "homogeneity", the one that applies to FRW spacetimes. Can you give a reference for this different definition of "homogeneity"? The standard term for what you're describing, AFAIK, is simply "spherical symmetry".

and given the finite volume inside the EH

The "volume" inside the EH is not necessarily finite; as I said before, it depends on what "volume" you are looking at. The 4-volume inside the EH is infinite, since it covers an infinite range of the t coordinate. Spacelike 3-volumes cut out of that 4-volume may be finite or infinite, depending on how they are cut.

and that it might be full of matter that has fallen in the BH on its way to the singularity

The portion of the spacetime that is occupied by the matter that originally collapsed to form the BH *is* full of matter on its way to the singularity. And this portion (at least in the idealized spherically symmetric case) *is* isometric to a portion of a collapsing FRW spacetime. That is the model that Oppenheimer and Snyder described in their 1939 paper. However, that only applies to the non-vacuum portion of the spacetime. I don't really think an analogy between the *vacuum* portion of the spacetime inside the EH and FRW spacetime is useful, but that may be just me.

There is something I can't fully understand about this dependence of spacetimes on the frame or the coordinate patch chosen to decide about their staticity or lack of it, when it is supposed to be something invariant and as you and other have insisted the KVFs shouldn't depend on the coordinates.

Staticity, by the standard definition, *is* coordinate-independent. See above.

I know at least in Riemannian geometry KVFs are defined globally so in a space there cannot exist regions with different KVFs

The KVF \partial / \partial t in Schwarzschild spacetime is not a "different KVF" in different regions. But any vector field on a manifold is a mapping between points in the manifold and vectors in a vector space, and different points may map to different vectors. In a manifold which has the timelike-spacelike-null distinction, i.e., where vectors have a "causal nature", that means the same vector field may map different points in the manifold to vectors with a different causal nature.

At least my discussion above suggests that there may be a dependence on the slicing, that is on the frame and coordinates chosen to have a KVF being timelike or spacelike.

No. Whether a KVF, or indeed *any* vector field, is timelike, spacelike, or null *at a given event* is an invariant, independent of coordinates. But the particular vectors which are mapped to different events by a vector field are different vectors, and may have a different causal nature.

consider this statement from the wikipedia page "spacetime symmetries" where it consideres Einsten static spacetime as a subcase of FRW metrics:
"For example, the Schwarzschild solution has a Killing algebra of dimension 4 (3 spatial rotational vector fields and a time translation), whereas the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric (excluding the Einstein static subcase) has a Killing algebra of dimension 6 (3 translations and 3 rotations). The Einstein static metric has a Killing algebra of dimension 7 (the previous 6 plus a time translation). "

The terminology here is sloppy; the "time translation" KVF is only timelike outside the horizon. This is why I made a point of saying before that, for this topic of discussion, you can't just quote statements without looking at the actual definitions and math behind them. The actual math is perfectly clear: the 4th KVF in Schwarzschild spacetime is timelike outside the horizon, null on the horizon, and spacelike inside it. I'm sorry that so many sources are sloppy about describing this, but that's why I've spent so much effort in this thread explicitly showing the actual math.

 

[PeterDonis]

the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric (excluding the Einstein static subcase) has a Killing algebra of dimension 6 (3 translations and 3 rotations).

I forgot to comment on this specifically. AFAIK, the standard definition of "homogeneity" for a spacetime is that there are 3 KVFs corresponding to spatial translations. The fact that those are *not* present in Schwarzschild spacetime is why I have been objecting to describing that spacetime as "homogeneous".

 

[PeterDonis]

"As a class of models with different values of the Hubble constant, the static universe that Einstein developed, and for which he invented the cosmological constant, can be considered a special case of the de Sitter universe where the expansion is finely tuned to just cancel out the collapse associated with the positive curvature associated with a non-zero matter density. "

This seems like sloppy terminology as well, since the de Sitter universe has *zero* matter density and a positive cosmological constant, so a model with *nonzero* matter density is not, properly speaking, a "special case" of it.

 

[Dale]

I see what you mean about the dependence on the slicing, and dealing with GR manifolds there should not be preferred slicing.

I wouldn't say that. If your GR manifold is everywhere vacuum then there should not be preferred slicing, but if your GR manifold has matter fields then the matter fields will disrupt the symmetry and may define a preferred slicing.

At least my discussion above suggests that there may be a dependence on the slicing, that is on the frame and coordinates chosen to have a KVF being timelike or spacelike.

The V in KVF is "vector". The timelike or spacelike character of a vector has nothing to do with the coordinates chosen, they remain timelike or spacelike in any coordinate chart. If it were not so, then they would not be vectors.

 

[erasrot]

I hope you find this question related with this thread topic. Let us assume that all the ideal conditions for the Oppenheimer-Snyder collapse are met, does it ever stop for any observer?

 

[PeterDonis]

I hope you find this question related with this thread topic. Let us assume that all the ideal conditions for the Oppenheimer-Snyder collapse are met, does it ever stop for any observer?

Yes.

 

[PAllen]

I hope you find this question related with this thread topic. Let us assume that all the ideal conditions for the Oppenheimer-Snyder collapse are met, does it ever stop for any observer?

A good trigger for a summary.

Anything you see (most noticeably for things far away) is an image from the past. That is all you can possibly know.

Talking about what is happening at a distance 'now' must be based on extrapolation and and some definition of 'now'.

Someone observing Oppenheimer-Snyder collapse from a distance never sees anything cross the event horizon. You can say that visually, the collapse appears to freeze. The is the physical observable. There are many plausible extrapolations to 'now' such that you may consider that a horizon has formed and the matter collapsed to a singularity. There are also definitions of 'now' such that this never happens.

For a free fall observer moving with the collapsing dust, the horizon is crossed and a singularity is reached after finite time on their wristwatch. In general, any radial free fall observer sees the collapse proceed to a singularity.