A question on the geometry of black holes

[Cerenkov]

No, that's not what I said. What I said is that our observable universe, in the limit as you go to the initial singularity, shrinks to a point. So does any finite-sized region of our universe.

I did not say that that point is somehow a "different" singularity from the initial singularity, or that each different finite region of our universe has its own singularity. Neither of those things are true. There is one initial singularity, and any finite-sized region will shrink to a point as that one initial singularity is approached.

Since the initial singularity is a spacelike line, it can of course also be considered as a continuum of points. If you want a heuristic for what those points "correspond" to in the universe proper, each such point represents a different comoving observer. But that doesn't mean each comoving observer has their own point-sized singularity: it means that each comoving observer corresponds to a point on the one spacelike line that is the one initial singularity.

Ah... now I might be getting it.

Are you saying that any finite volume of our universe will have an initial singularity which is point-like, but the entire volume of the universe (if it were possible to speak in those terms) will possess a spacelike line for the initial singularity?

That a point-like singularity is necessarily generated by the boundary of the finite volume?

Something like that?

 

[PeterDonis]

Are you saying that any finite volume of our universe will have an initial singularity which is point-like, but the entire volume of the universe (if it were possible to speak in those terms) will possess a spacelike line for the initial singularity?

That a point-like singularity is necessarily generated by the boundary of the finite volume?

No. Please read my posts #26 and #30.

 

[Cerenkov]

Better said, any observer can only see a point on the singularity, not the whole extent of it. (Note: it's only possible to see any of the singularity in principle - the universeis opaque that far back.)

Yes, forgive my loose usage of the word 'see'.

I'm aware that 'seeing' through the opaque plasma of the very early universe is not possible.

 

[Ibix]

Yes, forgive my loose usage of the word 'see'.

I'm aware that 'seeing' through the opaque plasma of the very early universe is not possible.

You're still seem to be missing the point, though. In this context there's nothing special about the singularity. The universe is currently infinite, and my observable universe is a patch of it, and yours is a very slightly different patch of it. Some alien trillions of light years away will also have a region of space to call its observable universe now, one which is completely disjoint from ours. The same was true yesterday (although all our observable universes were a bit smaller) and the day before and the day before, all the way back to the singularity. There is one singularity (which is a 3d spacelike surface, or at least the limit of it), we just have different parts of it "behind" us.

 

[Cerenkov]

No. Please read my posts #26 and #30.

Hmmm... to properly understand what you meant in those two posts I'd first have to understand what proper distance and comoving distance are and how they relate to one another.

Which I don't.

So, I'm sorry to say that for all the accuracy of your replies, they are as opaque to me as the plasma-filled early universe.

As I alluded to in post # 17, diagrams are useful for those who cannot do the math. But the Davis & Lineweaver diagrams which are often referred to in discussions like this are just as opaque to me too.

So, perhaps this discussion can go no further?

You can't explain to me what I'd like to know without using terms and diagrams that I can't understand and I can't understand the concepts involved without being able to understand those terms and the diagrams?

Is that a fair summary of where we are?

 

[Cerenkov]

You're still seem to be missing the point, though. In this context there's nothing special about the singularity. The universe is currently infinite, and my observable universe is a patch of it, and yours is a very slightly different patch of it. Some alien trillions of light years away will also have a region of space to call its observable universe now, one which is completely disjoint from ours. The same was true yesterday (although all our observable universes were a but smaller) and the day before and the day before, all the way back to the singularity. There is one singularity (which is a 3d spacelike surface, or at least the limit of it), we just have different parts of it in "behind" us.

That's helpful... I think.

Couldn't the blue line that I placed at the extreme left hand edge of the modified diagram be considered as just such a surface?

Each observer sees their own part of it as a point-like singularity, but it extends infinitely up and down along the vertical axis of the modified diagram.

Doesn't that satisfy the conditions of what you've just written?

 

[Cerenkov]

It's late here and I must log off.

But I thank you both for your patience and perseverance.

Until tomorrow.

 

[Ibix]

Couldn't the blue line that I placed at the extreme left hand edge of the modified diagram be considered as just such a surface?

I think your wording is a bit off if you are meaning the same as what we're saying.

Each observer sees their own part of it as a point-like singularity, but it extends infinitely up and down along the vertical axis of the modified diagram.

I don't think it's a good idea to say they see a point-like singularity, because the case can be made that they see a finite region of it (although it has zero size in some senses - singularities are not well behaved entities by definition). If you dropped "as a point-like singularity" from the bit I've quoted, I'd agree. Note that the big bang singularity is 3d (caveats about not actually being part of spacetime, so formally you need to consider the limits etc, apply), unlike the black hole singularity which is 1d.

It's late here

Likewise,but it's really hot so I'm awake and talking physics. I should try to sleep, I suppose...

 

[PeterDonis]

I'd first have to understand what proper distance and comoving distance are and how they relate to one another.

Which I don't.

The diagrams in Davis & Lineweaver show the difference. In terms of comoving distance, any two comoving observers are a constant distance apart. By convention, that distance is the proper distance between them "now". So a comoving observer that is just at our particle horizon "now" (i.e., at the edge of the funnel in the funnel diagram, if the funnel is centered on us) is about 46 billion light-years away from us in comoving distance. But unlike proper distance, that comoving distance stays constant--so as you move into the past, that comoving observer gets closer to us in terms of proper distance, but stays the same comoving distance away.

So comoving distance can be used as a measure of "distance" along the initial singularity: each point of the singularity corresponds to a different comoving observer. That's what the middle and bottom diagrams of Figure 1 in Davis & Lineweaver show. The comoving observers have worldlines that are vertical in those diagrams: each one stays at "the same point in space" in terms of comoving distance.

 

[PeroK]

It's late here and I must log off.

But I thank you both for your patience and perseverance.

Until tomorrow.

A singularity is where the mathematical model breaks down. The observable universe can't have expanded from a point in a physically meaningful way.

You can, however, mathematically map a finite volume to a point. And that may or may not make sense physically. But, that mapping has no inverse. So, in a sense it's not physically reversible.

Even if you work back to a point, there's no way to work forwards from a point. That's a singularity.

 

[Cerenkov]

I think your wording is a bit off if you are meaning the same as what we're saying.

I don't think it's a good idea to say they see a point-like singularity, because the case can be made that they see a finite region of it (although it has zero size in some senses - singularities are not well behaved entities by definition). If you dropped "as a point-like singularity" from the bit I've quoted, I'd agree. Note that the big bang singularity is 3d (caveats about not actually being part of spacetime, so formally you need to consider the limits etc, apply), unlike the black hole singularity which is 1d.

Likewise,but it's really hot so I'm awake and talking physics. I should try to sleep, I suppose...

Ibix,

If I keep referring to the initial singularity as point-like, that'll be because the first, unmodified diagram which I posted 'appears' to show one. But I do appreciate that looking at it from our God-like point of view outside of the universe is not the same as being an observer of it inside the universe itself. If that's what you meant about an observer seeing only a finite region of it, then point accepted.

So, could you a suggest a better and more accurate wording than point-like?

Cerenkov.

 

[PAllen]

Ibix,

If I keep referring to the initial singularity as point-like, that'll be because the first, unmodified diagram which I posted 'appears' to show one. But I do appreciate that looking at it from our God-like point of view outside of the universe is not the same as being an observer of it inside the universe itself. If that's what you meant about an observer seeing only a finite region of it, then point accepted.

So, could you a suggest a better and more accurate wording than point-like?

Cerenkov.

One can discuss the topology of limiting surfaces approaching a singularity. In that sense, the topology of the initial big bang singularity for an open universe (either flat or hyperbolic) is R3 meaning ordinary 3-space. This is simply because every isotropic surface that exists in the manifold has the topology (and is infinite in extent). For a closed universe, you can talk about the initial singularity being pointlike. The limiting surfaces are ever smaller S3 - 3-spheres. This limit can reasonably be taken to be a point.

In contrast, the approaching surfaces for a non-rotating spherically symmetric BH are S2 x R, that is the product space of a 2 sphere and a line. This is called a hypercylinder. Since the 2 sphere radius approaches 0 in the limit, you can reasonably think of the singularity as being a spacelike line.

 

[Cerenkov]

The diagrams in Davis & Lineweaver show the difference. In terms of comoving distance, any two comoving observers are a constant distance apart. By convention, that distance is the proper distance between them "now". So a comoving observer that is just at our particle horizon "now" (i.e., at the edge of the funnel in the funnel diagram, if the funnel is centered on us) is about 46 billion light-years away from us in comoving distance. But unlike proper distance, that comoving distance stays constant--so as you move into the past, that comoving observer gets closer to us in terms of proper distance, but stays the same comoving distance away.

So comoving distance can be used as a measure of "distance" along the initial singularity: each point of the singularity corresponds to a different comoving observer. That's what the middle and bottom diagrams of Figure 1 in Davis & Lineweaver show. The comoving observers have worldlines that are vertical in those diagrams: each one stays at "the same point in space" in terms of comoving distance.

Thank you Peter,

I appreciate that you are doing your best here, being rigorously accurate in your descriptions.

But please consider that a description that is itself beyond my capacity to understand, for all of its accuracy, fails to fulfil its purpose. Understanding does not come through it. Perhaps you recall that you once tried to walk me gently through the Davis & Lineweaver diagrams and after as short while I had to give up?

However, that result and my current confusion is neither your fault, the fault of the diagrams or even my fault. Without the proper training and without putting in all the necessary hard work how could I possibly be expected to understand them?

The terms Proper Distance and Comoving Distance are not understood by me. I first need to understand what they are and how they work separately before you can try to acquaint me with how they work together, relative to each other in the context of the D & L diagrams. (Which I have open in another tab and am looking at now in bemusement.)

But I'm not disappointed or put off by my limitations. Instead, prompted by my shortcomings I have an idea.

Over the years of my membership of this forum I've noticed that the D & L diagrams are the go-to resource for explaining much about the universe. Members are often directed to them and the resident experts of this forum hold them up as a kind of gold standard heuristic.

And yet, what of the Basic level members like myself, who cannot avail themselves of the understanding they can provide? Can their needs be better met or must they come to the same kind of grinding halt that has happened to me? I therefore offer a polite and tentative suggestion.

Is it in any way feasible to create a Beginner's Guide, couched at a Basic level, for these diagrams and so widen their usefulness to a larger audience?

Thank you,

Cerenkov

 

[Cerenkov]

One can discuss the topology of limiting surfaces approaching a singularity. In that sense, the topology of the initial big bang singularity for an open universe (either flat or hyperbolic) is R3 meaning ordinary 3-space. This is simply because every isotropic surface that exists in the manifold has the topology (and is infinite in extent). For a closed universe, you can talk about the initial singularity being pointlike. The limiting surfaces are ever smaller S3 - 3-spheres. This limit can reasonably be taken to be a point.

In contrast, the approaching surfaces for a non-rotating spherically symmetric BH are S2 x R, that is the product space of a 2 sphere and a line. This is called a hypercylinder. Since the 2 sphere radius approaches 0 in the limit, you can reasonably think of the singularity as being a spacelike line.

Hello and thank you PAllen.

You reply has touched upon another aspect of singularities that I've been grappling with.

I'm sufficiently au fait with the above diagram to realise that the Open and Flat universes are considered to be infinite in extent, while the Closed one is a finite volume. Therefore, I can appreciate how a pointlike (sorry Ibix) singularity can give birth to such a finite volume. But perhaps you can appreciate my confusion in trying to reconcile how an initial singularity relates to an Open and a Flat universe?

That which is infinite in extent cannot have had a finite point of origin. That's an impossibility. Or so it seems to me.

Thank you,

Cerenkov.

 

[Parthib Roy]

Thank you Peter,

I appreciate that you are doing your best here, being rigorously accurate in your descriptions.

But please consider that a description that is itself beyond my capacity to understand, for all of its accuracy, fails to fulfil its purpose. Understanding does not come through it. Perhaps you recall that you once tried to walk me gently through the Davis & Lineweaver diagrams and after as short while I had to give up?

However, that result and my current confusion is neither your fault, the fault of the diagrams or even my fault. Without the proper training and without putting in all the necessary hard work how could I possibly be expected to understand them?

The terms Proper Distance and Comoving Distance are not understood by me. I first need to understand what they are and how they work separately before you can try to acquaint me with how they work together, relative to each other in the context of the D & L diagrams. (Which I have open in another tab and am looking at now in bemusement.)

But I'm not disappointed or put off by my limitations. Instead, prompted by my shortcomings I have an idea.

Over the years of my membership of this forum I've noticed that the D & L diagrams are the go-to resource for explaining much about the universe. Members are often directed to them and the resident experts of this forum hold them up as a kind of gold standard heuristic.

And yet, what of the Basic level members like myself, who cannot avail themselves of the understanding they can provide? Can their needs be better met or must they come to the same kind of grinding halt that has happened to me? I therefore offer a polite and tentative suggestion.

Is it in any way feasible to create a Beginner's Guide, couched at a Basic level, for these diagrams and so widen their usefulness to a larger audience?

Thank you,

Cerenkov

I would like to second Cerenkov's suggestion here.

As another member who finds themselves reading these threads with a mix of fascination and bewilderment, I think a "Basic Level" or Beginner's Guide to the Davis & Lineweaver diagrams would be an incredible asset to the Physics Forums community.

The resident experts here do a fantastic job of maintaining rigorous accuracy, but for those of us without formal training in GR or cosmology, the jump from intuitive concepts to complex spacetime diagrams can feel like a vertical wall.

When foundational terms like Proper Distance and Comoving Distance aren't fully intuitive yet, trying to decipher how they warp and interact on a D&L plot is incredibly tough. A pinned, conceptual guide that breaks down these coordinates step-by-step—using simple analogies before diving into the geometry—would bridge the gap for a huge audience of casual learners here.

Thank you all for your ongoing patience with our questions!
also to @Cerenkov i would like to also suggest you another way out if you like to understand the explaination in diluted or clearer pace try using ai extension which can read the forum and you could seek or create summaries from it .I too am using similar methods as i too am a high schooler and do not have a full grasp at the concepts
Thanks,
Parthib Roy

 

[Bandersnatch]

Try this
https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/
It's not specifically about the Lineweaver and Davies paper, but introduces many of the concepts needed for reading those graphs.

 

[Cerenkov]

Thanks Bandersnatch,

Umm... if questions arise from the reading of this (as I'm sure they will) what's the best policy?

Bring those questions to this thread, start up a new one or some other option?

Wanting to do the right thing here.

Cerenkov.

 

[PeterDonis]

That which is infinite in extent cannot have had a finite point of origin.

It doesn't. As @PAllen said, the topology of the initial singularity for the open (and flat, though I don't think he included that case explicitly) is R^3, i.e., the same topology as ordinary Euclidean 3-space, i.e., infinite.

 

[PeterDonis]

Is it in any way feasible to create a Beginner's Guide, couched at a Basic level, for these diagrams

As another member who finds themselves reading these threads with a mix of fascination and bewilderment, I think a "Basic Level" or Beginner's Guide to the Davis & Lineweaver diagrams would be an incredible asset to the Physics Forums community.

I'm not sure how much more basic you can get than the diagrams themselves. Maybe someone else has a bright idea of how to simplify things further than that without actually distorting the physics, but I don't.

 

[PeterDonis]

The terms Proper Distance and Comoving Distance are not understood by me.

Did you actually read the post of mine that you quoted? You quoted it, but you didn't actually ask any questions about what it said. You just punted and said "not understood by me".

Explanation is always a two-way street. You have to make some effort to meet the explainer halfway.

 

[PeterDonis]

if questions arise from the reading of this (as I'm sure they will) what's the best policy?

Bring those questions to this thread, start up a new one or some other option?

Start a new thread, quoting whatever particular things in the Insights article you want to ask about.

 

[PeterDonis]

I would like to second Cerenkov's suggestion here.

Did you read my post #39 (which Cerenkov quoted)? Do you have specific questions about what it said?

 

[Cerenkov]

Did you actually read the post of mine that you quoted? You quoted it, but you didn't actually ask any questions about what it said. You just punted and said "not understood by me".

Explanation is always a two-way street. You have to make some effort to meet the explainer halfway.

Yes, I read it.

But your comments about effort need to be put into their proper context. A context you are not aware of and which I was loathe to reveal. But you have forced my hand and so I must now defend myself against your accusation of not putting in the effort.

In 1997 I fell ten feet and knocked myself out for 45 minutes. After that head trauma I was diagnosed with an Atypical Endogenous Depression and I will be on medication to moderate the head injuries effects for the rest of my life. The chemistry of my brain was irrevocably altered by the impact of my head on solid ground. In the following months, as my brain chemistry oscillated wildly, I lost control of my limbs, my bowels and my sense of balance. There was a consequent loss of dignity associated with that was traumatising too.

That event ended my marriage and my career but not my enthusiasm for astronomy and cosmology.

I suffer daily from extreme fatigue and have to sleep at irregular intervals. I cannot handle even modest amounts of stress and must avoid any and all stress-making scenarios. I am hugely dependent on my partner and can only function properly for a few hours every day.

This is the proper context in which comments about my efforts should be seen.

Apparently one of the effects sometimes seen in people who have undergone severe head injuries is an extreme defensiveness about their condition. Well, lo and behold! I'm feeling VERY defensive right now and you are the cause of it.

Given the turn of events in this thread I think it best if I take up Bandersnatch's idea and read up about the concepts underpinning the D & L diagrams, returning to this forum when I am in a better frame of mind.

Cerenkov.