Exploring Spacetime in Black Holes

[mikeeey]

Hello every one .
Simple question , What happens to the ended spacetime fabric in the singularity poing of the black hole if the black hole starts to move in spacetime ? Would the dead spacetime fabric at that point return to the regular shape of space time fabric ? ( as we know spacetime at sigularity point becomes meaningless or tears up )

 

[PeterDonis]

the ended spacetime fabric

What do you mean by "spacetime fabric"? This is not a recognized concept in GR.

the singularity poing of the black hole

A black hole's singularity, strictly speaking, is not part of spacetime at all. It certainly is not a point. Different types of black holes have different geometries near their singularities; the simplest, the non-rotating Schwarzschild hole, has a singularity which is, heuristically, a spacelike line, i.e., it acts like a moment of time, not a place in space.

if the black hole starts to move in spacetime

A black hole is not like an ordinary object, and you have to be very careful in defining what you mean if you are going to try to think of it as "moving".

You labeled this thread as "A", which indicates graduate-level understanding of the subject matter. That is clearly not the case, so I have re-labeled this thread as "B". The "B" level answer to your question is basically that the question itself is ill-formed. My comments above give some indications as to why.

 

[mikeeey]

My friend , i study advanced mathematics , but i saw a video speaks about the meaningless spacetime in sigularity point where things start breaking down of the concepts , i will change my phrase [ what happens to that instantaneous singilarity point (where all infinite densed matter lives in it ) when a black hole globally would have a motion ( i mean global view like an object starts moving ( geodesic ) in general spacetime "grid ") , I am not talking about rotating about it self ( axis of symmetry ) . In math i think there is a geodesic language for linear momentum

 

[mathman]

From the outside a black hole is a very heavy, dense object. It will move through space (more or less) like any other heavy, dense object.

The inside is an open question. The description you gave is based on general relativity, where quantum theory is not considered. However when trying to consider both theories, it all breaks down and no one really knows what is going on.

 

[PAllen]

From the outside, motion of a BH is reasonably well defined, and in fact the first approaches to deriving geodesic motion from the field equations were done by Einstein and collaborators using black holes (even though Einstein never believed they would really form in our universe, they were a convenient model of a pointlike mass). The upshot is is that a BH moves, to extremely high precision, the same as something that is almost a BH, or more simply, similar to a neutron star.

 

[PeterDonis]

i saw a video

Please give a reference--either a link or at least a description of what video and where you saw it. And bear in mind that pop science videos are not appropriate sources here on PF, nor are they good sources for actually learning science.

what happens to that instantaneous singilarity point

The singularity is not a point. As I said before, it's a spacelike line. The closest reasonably intuitive concept is a moment in time, not a place in space. And strictly speaking, the singularity itself is not even part of the spacetime.

where all infinite densed matter lives in it

The singularity is not a place where infinitely dense matter is. A black hole, at least the idealized model of one we are talking about here, is vacuum everywhere; there is no matter.

when a black hole globally would have a motion

As PAllen pointed out, a black hole can be viewed as "moving" only in an asymptotic sense, i.e., if you ignore its internal structure and just treat it as a compact object with a particular mass in an asymptotically flat spacetime. If you go into enough detail to look at the hole's internal structure, you can no longer view it as an object moving in the ordinary sense.

For all of the reasons given above, once again, the question you are asking is not well posed. Please consider that very carefully.

 

[pervect]

Hello every one .
Simple question , What happens to the ended spacetime fabric in the singularity poing of the black hole if the black hole starts to move in spacetime ? Would the dead spacetime fabric at that point return to the regular shape of space time fabric ? ( as we know spacetime at sigularity point becomes meaningless or tears up )

I would say that objects can move in space, but I don't think it's all that sensible to say they move in space-time. A classical space-time construct, using the block universe philosophy, would have past and future both as part of the space-time geometry. I don't see any sensible way that one could say the geometry moves. The geometry simply is.

Perhaps there is some alternative other than the block universe philosophy, one which makes the idea of motion in space-time more sensible than it is in the block universe philosophy, but I can't imagine what it would be.

In the block universe view, the only difference between a moving black hole and a stationary one would be one's viewpoint. The fundamental geometry is unchanged , one can regard the difference as a matter of perspective.

 

[Stephanus]

A black hole's singularity, strictly speaking, is not part of spacetime at all. It certainly is not a point. Different types of black holes have different geometries near their singularities; the simplest, the non-rotating Schwarzschild hole, has a singularity which is, heuristically, a spacelike line, i.e., it acts like a moment of time, not a place in space.

Can I ask a question here?
I'd like to ask soo many questions regarding this post.
- A black hole singularity is not part of spacetime
- A black hole singularity is not a point
- A black hole singularity is a spacelike line
- A black hole singularity acts like a moment of time
- A black hole singularity is not a place in space

I don't know where to start first, perhaps this.
What is black hole singularity?
Supposed a black hole, 1 kilo ton
Then an object, say a rocket (1 ton) falls inside EH, now the black hole mass is 1.001 ton, right.
but it's still intact. Is the rocket part of the singularity?
Now, the rocket falls deeper and deeper and pass by the, what they say by, "ouch radius", that is the difference of 9.8m² in 1.8 m, and the rocket get spaghettized
Does in this phase the rocket belongs to the singularity?
Or everything inside EH is undefined?
Just WHEN will the rocket belong to the singularity? Or the "when" word here is wrong?
Thanks

 

[PeterDonis]

Can I ask a question here?

These questions are getting beyond the "B" level. I think it would be a good thing for you first to decide that you're willing to move up a level and take on some more in-depth sources, and spend some time doing so.

I'll give answers to some of your questions in what follows, but after that I think you will need to start a new thread at at least the "I" level to go deeper into these questions, which means you will first need to acquire some background knowledge at that level.

Is the rocket part of the singularity?

No. The EH is not the singularity, nor is the region of the black hole inside the EH. But as you go deeper and deeper inside the hole (inside the EH), to radial coordinates that get closer and closer to $r = 0$, spacetime curvature increases without bound. The limit point, $r = 0$, is called "the singularity", but it is not actually part of spacetime--spacetime itself is an open set, and open sets do not include limit points like $r = 0$. (This is a very rough, heuristic way of describing a fairly advanced piece of differential geometry.) Heuristically, we say that "spacetime curvature is infinite" at $r = 0$, but what we really should say is just that curvature increases without bound as $r$ approaches zero, but curvature is still finite for any $r > 0$, which means at any point that is actually part of spacetime.

the, what they say by, "ouch radius", that is the difference of 9.8m2 in 1.8 m, and the rocket get spaghettized
Does in this phase the rocket belongs to the singularity?

No. At some point tidal gravity (which is another name for "spacetime curvature") will spaghettify the rocket, yes. But this is still not the singularity. The rocket has a finite material strength, so at some finite $r$ greater than zero, tidal gravity will exceed that finite material strength and tear the rocket apart.

Or everything inside EH is undefined?

Certainly not. The region inside the EH, for $r > 0$, is a perfectly well-defined region of spacetime, at least in the classical model.

Just WHEN will the rocket belong to the singularity?

Never. The rocket can never actually experience $r = 0$, even if it could somehow resist tidal gravity of unbounded strength, because that limit point is not part of spacetime, as above.

 

[Stephanus]

Thanks PeterDonis for the answer.

Never. The rocket can never actually experience $r = 0$, even if it could somehow resist tidal gravity of unbounded strength, because that limit point is not part of spacetime, as above.

Perhaps this can cause a confusion here. Because once spaghettized, it's not a rocket anymore.
Can I ask a simple question?
A. Can a hydrogen atom experience $r = 0$?
Or, once the atom is in $r = 0$, then it's not the part of our space time?
B. Can a PHOTON experience $r = 0$?
I'm getting trouble trying to imagine singularity. Something has mass, yet does not have space dimension (r=0), and does it have time dimension?

 

[Ibix]

I think the point is that trying to imagine the singularity doesn't make sense. It's another concept like the perspective of someone moving at light speed.

The difference here is that we think singularities are a sign of the failure of GR. As Peter says, GR is based on spacetime being an "open set", which can't include singularities. Then you work out the maths of a spacetime containing mass and it predicts singularities. Most people take that to mean that the maths is strongly hinting that there's something not quite right about the theory in extreme circumstances. Hence the search for quantum gravity.

 

[PeterDonis]

once spaghettized, it's not a rocket anymore.

True, I should have been clearer. No object can ever experience $r = 0$ inside a black hole--at least not if we use the idealized classical model we are using in this discussion.

an a hydrogen atom experience $r = 0$?

Yes, because a hydrogen atom is not a black hole. A black hole is a different spacetime geometry from any ordinary object, and in that different spacetime geometry, $r = 0$ cannot be experienced by any object.

Can a PHOTON experience r=0r=0r = 0?

In an ordinary spacetime, yes. Inside a black hole, no.

I'm getting trouble trying to imagine singularity.

That's because, as I said, you're trying to use "B" level imagination an intuition to understand a concept that is at least at the "I" level (and possibly higher than that). You need, as I said before, to spend time learning more advanced General Relativity in order to retrain your imagination and intuition. You should not expect to be able to imagine what the spacetime geometry of a black hole is like at your current level of knowledge, because that spacetime geometry has no counterpart in ordinary experience.

Something has mass, yet does not have space dimension

I did not say a black hole does not have "a space dimension". I just said the particular locus $r = 0$ is not part of the black hole spacetime. But any $r > 0$ is part of the spacetime, as I also said. As above, you should not expect this to be obvious to your imagination or intuition at your current level of knowledge. But it's true.