A question on the geometry of black holes

[Parthib Roy]

So i always saw those graphical diagrams of blackholes where we can an opening at the top and the cannal goes deeper into the space time fabric revealing its untra massive core

but this is a 2d depiction of a 3d model ,Black holes are not circular holes in space time fabric, they are spherical ,so my question is in a 2D model we can see the end of the hole but where does the end of the hole exist in a 3d sphere ,it cant be at there geometric center right(as black holes are smaller than there parent stars)?? or it exist in some other plain or dimention ??

 

[javisot]

So i always saw those graphical diagrams of blackholes where we can an opening at the top and the cannal goes deeper into the space time fabric revealing its untra massive corebut this is a 2d depiction of a 3d model ,Black holes are not circular holes in space time fabric, they are spherical ,so my question is in a 2D model we can see the end of the hole but where does the end of the hole exist in a 3d sphere ,it cant be at there geometric center right(as black holes are smaller than there parent stars)?? or it exist in some other plain or dimention ??

What do you mean by "at there geometric center"?

That's indeed a 2D representation and you need to extrapolate it to more dimensions, but you also have to remember that this 2D surface is spacetime, not just space. The center isn't just a point in space.

 

[Ibix]

You can't extend that kind of picture to a black hole interior, unfortunately. Assumptions made during the drawing fail at the event horizon, so they only work outside.

The interiors of black holes are rather odd places. They are actually infinite in extent and they do not have a center. All matter falling into one ends up at the singularity, but that isn't at the center - it is more like a moment in time, a finite time ahead of when you cross the horizon. That's one way of looking at why you can't avoid it - you can't avoid tomorrow morning either.

You can draw maps of the interior of black holes, although they are all rather abstract and are extremely distorted because of the problems of drawing extremely curved spacetime on a flat piece of paper. I can dig one out later and attempt to explain its features if you like.

Also, note that this is what General Relativity says. We have reason to believe that GR stops being an accurate picture of reality somewhere inside a black hole, but unfortunately we don't have a better theory yet.

 

[Parthib Roy]

You can't extend that kind of picture to a black hole interior, unfortunately. Assumptions made during the drawing fail at the event horizon, so they only work outside.

The interiors of black holes are rather odd places. They are actually infinite in extent and they do not have a center. All matter falling into one ends up at the singularity, but that isn't at the center - it is more like a moment in time, a finite time ahead of when you cross the horizon. That's one way of looking at why you can't avoid it - you can't avoid tomorrow morning either.

You can draw maps of the interior of black holes, although they are all rather abstract and are extremely distorted because of the problems of drawing extremely curved spacetime on a flat piece of paper. I can dig one out later and attempt to explain its features if you like.

Also, note that this is what General Relativity says. We have reason to believe that GR stops being an accurate picture of reality somewhere inside a black hole, but unfortunately we don't have a better theory yet.

Ahh thats a even better explanation than i expected .At first i would like to thank you for your explanation it really makes the idea a lot clearer for me .also i would like to ask you one more thing ,could you clarify by what u mean as "it is more like a moment in time, a finite time ahead of when you cross the horizon. That's one way of looking at why you can't avoid it - you can't avoid tomorrow morning either." do you mean that beyond the event horizon the object falling down into a black hole slows down to such an extent that time practically freezes for them and it feels like the object is falling forever into until it is completely disintegrated ??

 

[PeroK]

Ahh thats a even better explanation than i expected .At first i would like to thank you for your explanation it really makes the idea a lot clearer for me .also i would like to ask you one more thing ,could you clarify by what u mean as "it is more like a moment in time, a finite time ahead of when you cross the horizon. That's one way of looking at why you can't avoid it - you can't avoid tomorrow morning either." do you mean that beyond the event horizon the object falling down into a black hole slows down to such an extent that time practically freezes for them and it feels like the object is falling forever into until it is completely disintegrated ??

It's not like that. A singularity is when a mathematical model breaks down. It's not a physical thing. Once you cross the event horizon, you only have a finite amount of time before the mathematical model breaks down.

Most physicists expect that a theory of quantum gravity will explain what really happens below the event horizon.

 

[Ibix]

do you mean that beyond the event horizon the object falling down into a black hole slows down to such an extent that time practically freezes for them and it feels like the object is falling forever into until it is completely disintegrated ??

No. If you fell into a black hole the mass of the Sun (and if GR were correct which it probably isn't!) you would reach the singularity about fifteen microseconds after crossing the event horizon by your watch. For a billion sun mass super massive black hole, it would take about twenty five minutes.

However, the singularity isn't a place in space. It is not a point of infinite density or anything like that.

Remember that GR isn't a theory about space, it's a theory about spacetime. If you draw a map of spacetime on a piece of paper you might say left on the map is to the left in the world, right is to the right, but up and down on the map correspond to moving into the future or the past. A horizontal line on the map is all of space (or at least all of space that happens to be on one straight line) at one time, and a horizontal line just above it is the same but of space a little bit later.

GR says that if you fall into a black hole, the map has an edge at the top that isn't just "got bored of drawing". That's the singularity - an edge to the map at the top, in the future. You can reach it in finite time and then GR won't tell you anything more - you fell off the edge of the only map we know how to draw. Well, tidal forces would shred you first, but your remains would fall off the edge of the map.

That's basically why we suspect GR isn't quite right - we suspect that a physical theory that describes something you can do but then says "eh, I dunno" part way through isn't quite the truth.

 

[PeterDonis]

the singularity isn't a place in space. It is not a point of infinite density or anything like that.

It's worth noting, though, that even though the interior of a black hole is vacuum, the spacetime curvature does increase without bound as the singularity is approached. So a person who falls through the horizon will find their body becoming increasingly deformed, and ultimately torn apart, in the finite time by their clock before they reach the singularity. Even if GR breaks down before the singularity is actually reached, and some other physics like quantum gravity takes over, it's still highly likely that the person's body would be destroyed before that point is reached.