Is it possible to reach the singularity?

[ExecNight]

The question is;

After an object goes through the event horizon, is it possible for the object to reach the singularity?

As far as i know, singularity, bends space down and actually space moves faster than light towards the singularity. But what tells us that the singularity's bending has a limit? Would it keep bending, and creating more space over time inside the event horizon.

The more correct way of wording would be, doesn't the singularity become the arrow of time once the object is inside the event horizon. Which would be only reachable if you could move mass at the speed of light, which is impossible?

 

[stevendaryl]

The question is;

After an object goes through the event horizon, is it possible for the object to reach the singularity?

It's more than possible---it's certain. Once inside the event horizon, the singularity is as inevitable as next Monday.

 

[ExecNight]

It's more than possible---it's certain. Once inside the event horizon, the singularity is as inevitable as next Monday.

Yes of course, but first part of the question is, shouldn't the object first lose its mass, and reach c, to hit the singularity?

 

[stevendaryl]

Yes of course, but first part of the question is, shouldn't the object first lose its mass, and reach c, to hit the singularity?

No. That's the point of my "next Monday" analogy: if you're inside the event horizon, the singularity is in your future. Just sitting around, you'll reach it, in the same way that you'll reach next Monday no matter what you do.

 

[anorlunda]

All that presumes that there is a singularity. As far as I know, that is just speculation. We can't know for certain anything that happens inside the EH.

But it is also often heard that predicting a singularity just means that our models of the laws of physics break down, thus preventing a singularity from forming in the first place.

 

[ExecNight]

I will try to elaborate;

About your monday analogy, When say i start counting 1 to 10, it is certain i will reach 10 very quickly. But things change when no rules are given. I can go with 1/2,2/3,3/4 and wouldn't even reach 1, let alone 10 forever.

The question came from a thought, if space moves say at 2c on the edge of the event horizon, it would then be moving around 4c close to the singularity, and say 8c even closer. But then, between these accelerating space, More space should be created in the process, since we can't have an area that there is no space in between different speeds of moving space.

I might not be explaining myself clearly, sometimes hard to put into words what you think.

 

[Nugatory]

The question came from a thought, if space moves say at 2c on the edge of the event horizon, it would then be moving around 4c close to the singularity, and say 8c even closer. But then, between these accelerating space, More space should be created in the process, since we can't have an area that there is no space in between different speeds of moving space.

That's not how the curved spacetime inside the event horizon behaves. Space doesn't "move" there or anywhere else, so you're starting from a mistaken premise.

We have a number of threads describing what happens to someone falling into a black hole and how long it takes to reach the singularity. It doesn't take long.

 

[stevendaryl]

All that presumes that there is a singularity. As far as I know, that is just speculation. We can't know for certain anything that happens inside the EH.

Of course not. But we do know what General Relativity predicts, and GR is not "just speculation".

 

[stevendaryl]

I will try to elaborate;

About your monday analogy, When say i start counting 1 to 10, it is certain i will reach 10 very quickly. But things change when no rules are given. I can go with 1/2,2/3,3/4 and wouldn't even reach 1, let alone 10 forever.

Well, General Relativity not only says that you will eventually reach the singularity, it predicts how long it will take. From the point of view of the infalling observer, it's over pretty quickly (unless the black hole is extremely massive).

 

[jbriggs444]

Well, General Relativity not only says that you will eventually reach the singularity, it predicts how long it will take. From the point of view of the infalling observer, it's over pretty quickly (unless the black hole is extremely massive).

To be overly picky, it says that you get arbitrarily close in finite bounded time. Since there is no point in the manifold which is "the singularity", it is hard for the theory to say that you actually reach such a point.

 

[stevendaryl]

To be overly picky, it says that you get arbitrarily close in finite bounded time. Since there is no point in the manifold which is "the singularity", it is hard for the theory to say that you actually reach such a point.

Fair enough. But take an pragmatic view of "being crushed by the singularity", such as: "Your body is compressed to the size of the head of a pin". That certainly happens in a finite amount of time.

[edit] Actually, that's not true; because of tidal forces, you're stretched, rather than compressed...But the point is: take some concrete criterion for being thoroughly messed up by spacetime curvature, and that happens in finite time.

 

[anorlunda]

Of course not. But we do know what General Relativity predicts, and GR is not "just speculation".

I don't mean to be pedantic but the prediction of a singularity can be interpreted as saying that GR does not apply in that region. Perhaps QM applies, but since GR and QM don't dance well, we don't know what should apply; LQG?

Shouldn't students be taught that we know GR applies outside the EH, but we don't know what applies inside the EH? Instead, we show Penrose diagrams that depict GR applying all the way up to and including the singularity. Doesn't that falsely blur the boundary between what we believe and what we know?

 

[PeroK]

I might not be explaining myself clearly, sometimes hard to put into words what you think.

If you can't put something in words, put it in mathematics!

 

[PeterDonis]

singularity, bends space down

This is not correct. See below.

space moves faster than light towards the singularity

This is a heuristic interpretation that is sometimes used (look up the "river model" of black holes), but it's not something you can use to draw inferences from the way you are trying to do.

doesn't the singularity become the arrow of time once the object is inside the event horizon

No. The singularity is a moment of time, which is to the future of all other moments inside the horizon.

Which would be only reachable if you could move mass at the speed of light

Aside from the errors pointed out above, I'm not sure how you are deducing this from anything being "the arrow of time". You might have a more general misunderstanding of how spacetime geometry works, apart from the specific question you are asking about black holes and the singularity.

if space moves say at 2c on the edge of the event horizon, it would then be moving around 4c close to the singularity, and say 8c even closer. But then, between these accelerating space, More space should be created in the process, since we can't have an area that there is no space in between different speeds of moving space.

None of this is correct.

 

[ExecNight]

The question came from a thought, if space moves say at 2c on the edge of the event horizon, it would then be moving around 4c close to the singularity, and say 8c even closer. But then, between these accelerating space, More space should be created in the process, since we can't have an area that there is no space in between different speeds of moving space.

None of this is correct.

d s^2 = - \, d t_{\rm ff}^2 + ( d r - v \, d t_{\rm ff} )^2 + r^2 ( d \theta^2 + \sin^2\theta \, d \phi^2 )

Is this not correct?

 

[stevendaryl]

I don't mean to be pedantic but the prediction of a singularity can be interpreted as saying that GR does not apply in that region. Perhaps QM applies, but since GR and QM don't dance well, we don't know what should apply; LQG?

Shouldn't students be taught that we know GR applies outside the EH, but we don't know what applies inside the EH? Instead, we show Penrose diagrams that depict GR applying all the way up to and including the singularity. Doesn't that falsely blur the boundary between what we believe and what we know?

Yes, you can take the singularity as evidence that GR is incomplete. But there is no actual singularity at the event horizon, so there is no particular reason to think that the EH is where GR stops working.

 

[PeterDonis]

Is this not correct?

If you're using Painleve coordinates (which is the coordinate chart that underlies the "river model" that I referred to before), the equation you wrote down is correct. But that's because of your choice of coordinates. "Space" is not a physical thing in GR; only spacetime is. "Space" is an artifact of how you choose your coordinates. So saying "space is moving inward" because a quantity $v$ appears in the metric you wrote down is not describing something physical that's happening; it's describing an artifact of your coordinates. But you were trying to interpret it as something physical that was happening, and infer from that something else. That is what is not correct.

(Also, even in the coordinates in question, $v$ is not $2c$ just inside the horizon. At the horizon, $v = c$; just inside the horizon, $v$ will be just a little bit greater than $c$.)

 

[ExecNight]

If you're using Painleve coordinates (which is the coordinate chart that underlies the "river model" that I referred to before), the equation you wrote down is correct. But that's because of your choice of coordinates. "Space" is not a physical thing in GR; only spacetime is. "Space" is an artifact of how you choose your coordinates. So saying "space is moving inward" because a quantity $v$ appears in the metric you wrote down is not describing something physical that's happening; it's describing an artifact of your coordinates. But you were trying to interpret it as something physical that was happening, and infer from that something else. That is what is not correct.

(Also, even in the coordinates in question, $v$ is not $2c$ just inside the horizon. At the horizon, $v = c$; just inside the horizon, $v$ will be just a little bit greater than $c$.)

I get your point, but physicist use the wording "gravity", although they all know there is no gravity, only curvature of space-time.

I know your future light cone can't contain anything other than the singularity, too.

Trying to get on the same page;

The geometry of space-time inside the event horizon bends towards the singularity and all possible paths now lead to the singularity.
Once inside the event horizon no matter which direction you accelerate you can only move towards the singularity faster.

Here is what's bugging me,
If you stand at rest inside the event horizon, with respect to the singularity, you shouldn't reach it. But time-like and space-like coordinates switch, so since you can't stop time, you move towards the singularity anyway.

Now this turns space, into something you move through constantly no matter what you do, and space becomes relative between observers with different relative speeds.

But that makes reaching the singularity, reaching the end of time. And in our universe space-time, an object can't reach it, since mass can't accelerate to c.

Thus, the original question, can an object reach the singularity.

 

[PeterDonis]

physicist use the wording "gravity", although they all know there is no gravity, only curvature of space-time

No, physicists use the word gravity, in the context of GR, to refer to the curvature of spacetime. In other words, they use the word to refer to a particular mathematical model. And they don't draw inferences from the word, they draw them from the mathematical model.

The geometry of space-time inside the event horizon bends towards the singularity

This doesn't correspond to anything in the math.

all possible paths now lead to the singularity

More precisely, all possible timelike and lightlike paths inside the horizon lead to the singularity. Yes, that's true, and it's one way of unpacking what it means to say that the singularity is a moment of time that is to the future of all other moments inside the horizon.

Once inside the event horizon no matter which direction you accelerate you can only move towards the singularity faster.

"Faster" in the sense of "will take less time by your clock to reach the singularity". Yes, that's true.

If you stand at rest inside the event horizon

You can't. There are no timelike paths inside the horizon that "stand at rest" in the sense you mean (staying "at the same distance" from the singularity). The singularity is a moment of time in your future if you are inside the horizon. You can't "stand at rest" relative to it any more than you can "stand at rest" relative to next Tuesday.

time-like and space-like coordinates switch

Only in a particular coordinate chart, so this is an artifact of coordinates, not something physical that is happening. (Note, btw, that the coordinates for which this artifact is present are not the ones you wrote down earlier, with $t_{ff}$.)

The rest of your post just builds on your mistaken understanding as given above.

can an object reach the singularity

Yes, because the singularity is a finite time in your future, just like next Tuesday (although it's a much shorter time once you're inside the horizon, at least for most holes we expect to find), and you can reach next Tuesday (and in fact you can't avoid it).

 

[ExecNight]

Hmm, internet is toxic like that. Know any online courses that can correct this misunderstanding? Because, obviously most stuff on the internet is just dumbed down stuff and really seems too illogical to me, hence comes all this frustration and questions..

This knowledge, don't let me ask it, that makes any sense to you.

 

[PeterDonis]

Know any online courses that can correct this misunderstanding?

I would suggest Carroll's online lecture notes:

https://arxiv.org/abs/gr-qc/9712019

He has also published a book which is an expanded version of these notes.

Chapter 7 discusses the Schwarzschild solution and black holes. Towards the end of the chapter (starting on p. 186 in the online version) he derives the Kruskal coordinate chart, which is the best one to use for understanding the causal structure inside the horizon. He doesn't explicitly point out all of the things I've said in this thread, but they are much more evident and easier to grasp if you look at the Kruskal chart.