What Happens Inside BH Event Horizon?

[kochanskij]

TL;DR Summary

What would a person inside a large non rotating black hole experience?

I have read about the spaghettification of objects due to tidal forces as they get close to the singularity. Gravity at your feet is stronger than at your head, so you get stretched and pulled apart. In this case, the singularity is a point in space.
But I also read about the time coordinate and the radial space coordinate becoming interchanged inside the event horizon. The singularity becomes an event in the future rather than a point in space. The space inside the horizon is a tiny self contained empty universe - a finite but unbounded 3D space, that shrinks until it becomes a point of zero size. This is the singularity, an event in time.
Which case is correct? Would you get stretched like spaghetti or crushed from all directions as the volume of space becomes less than your volume?

 

[PeterDonis]

I also read about the time coordinate and the radial space coordinate becoming interchanged inside the event horizon.

This is only true in one particular coordinate chart. It is not telling you anything useful about the actual spacetime geometry inside the horizon; it's only telling you about a particular property of that particular coordinate chart.

The singularity becomes an event in the future rather than a point in space.

Not "becomes", "is". More precisely, it's a moment of time in the future--this moment is not a single event because it's not a single point, it's a spacelike line. Different objects can "hit" the singularity at different "places", just as different objects can pass through the same moment of time at different places.

The space inside the horizon is a tiny self contained empty universe - a finite but unbounded 3D space, that shrinks until it becomes a point of zero size.

This is not correct. What you are describing is the geometry of a contracting 3-sphere (such as the geometry of a closed universe contracting to a Big Crunch), and that is not what the geometry of spacetime inside the black hole is like. (It is what the geometry inside the collapsing object that originally formed the hole is like, but nobody who falls into the hole will ever see that geometry; the collapse will have finished before they could ever reach it.)

Would you get stretched like spaghetti

Yes, in some directions.

or crushed from all directions

Not in all directions, but you will get crushed in some directions.

as the volume of space becomes less than your volume?

This is not why you get crushed in some directions. See above.

 

[kochanskij]

This is only true in one particular coordinate chart. It is not telling you anything useful about the actual spacetime geometry inside the horizon; it's only telling you about a particular property of that particular coordinate chart.Not "becomes", "is". More precisely, it's a moment of time in the future--this moment is not a single event because it's not a single point, it's a spacelike line. Different objects can "hit" the singularity at different "places", just as different objects can pass through the same moment of time at different places.This is not correct. What you are describing is the geometry of a contracting 3-sphere (such as the geometry of a closed universe contracting to a Big Crunch), and that is not what the geometry of spacetime inside the black hole is like. (It is what the geometry inside the collapsing object that originally formed the hole is like, but nobody who falls into the hole will ever see that geometry; the collapse will have finished before they could ever reach it.)Yes, in some directions.Not in all directions, but you will get crushed in some directions.This is not why you get crushed in some directions. See above.

Thank you for the clarification of my misunderstandings. But I'm still trying to picture what a person inside the BH would see and feel. Since the singularity is space like and in the future, he couldn't point towards it, right? Why would he experience tidal forces and stretching? Isn't that a result of a dense mass at a place in space? Why should gravity be stronger on his feet than his head? Don't his head and feet hit the singularity at the same time, just like your whole body reaches Monday at the same time?

 

[Orodruin]

Since the singularity is space like and in the future, he couldn't point towards it, right?

No, he could not.

Why would he experience tidal forces and stretching?

Because those are the result of spacetime curvature and spacetime curvature is non-zero. It is non-zero also outside of the horizon and also objects outside the horizon experience tidal forces. That is why we have … tides.

Isn't that a result of a dense mass at a place in space?

No. It is the result of spacetime curvature. Spacetime curvature depends on the geometry of spacetime, which depends both on the initial conditions as well as the distribution of matter in spacetime.

Don't his head and feet hit the singularity at the same time, just like your whole body reaches Monday at the same time?

What do you mean by ”same time”? This is coordinate dependent.
Edit: It is true that the head and feet hit the singularity at spacelike separation.

 

[Ibix]

Why would he experience tidal forces and stretching?

I'm afraid that the event horizon is where trying to think intuitively about Einstein's gravity as if it were a mathematically more complex version of Newtonian gravity fails hard. You are thinking that tidal forces relate to how far you are from the source of gravity - this is no longer true inside the horizon. There's also no uniquely defined global notion of time any more (there is one in Schwarzschild spacetime outside the event horizon), and this turns out to mean that there's also no notion of gravitational potential, which means you can't think of gravity as a force - it's only spacetime curvature.

So yes, your head and feet will continue to attempt to separate. You can't attempt to characterise it in terms of different gravitational pull, though. Formally, it's characterised by geodesic deviation - the notion that "going straight ahead in spacetime" doesn’t mean quite the same direction to your head as it does to your toes. This induces some stress in your body to try to drag your toes and your head off their "natural" paths and on to the path of your center of mass. The effect grows without bound as you approach the singularity and eventually rips you apart.

Note that you can use the same reasoning above the horizon - it's just usually more convenient there to reason in more familiar terms.

 

[kochanskij]

Thank you for explaining this misunderstanding I had of gravity inside a black hole. So what would I see and feel while inside? I would be weightless in my free fall? I will feel increasing tidal forces no matter how I orient my body? I can't see or point to the singularity? Am I in a self contained tiny finite 3D universe? Can I see the outside universe or point toward outside? If another object falls across the horizon, where would I see it appear or come from?
(I'm not actually planning on jumping into a black hole!)

 

[Orodruin]

So what would I see and feel while inside?

You would see light from the outside of the black hole.

I would be weightless in my free fall?

Unless you accelerate using a rocket or similar. Just like outside the black hole.

Am I in a self contained tiny finite 3D universe?

What does this mean?

I will feel increasing tidal forces no matter how I orient my body?

Yes.

I can't see or point to the singularity?

Can you point to the future?

If another object falls across the horizon, where would I see it appear or come from?

You would see it even before it passes the horizon. The horizon determines from where light cannot escape the black hole, it is not a separator preventing light from coming in.

 

[Ibix]

Am I in a self contained tiny finite 3D universe?

Space inside a black hole, for at least some definitions of space, is infinite in extent.

Can I see the outside universe or point toward outside?

You can see outside, although I think it's aberrated into a tiny patch of sky behind you (if you fell in feet first and didn't reorient, 'behind you' means above your head, here).

If another object falls across the horizon, where would I see it appear or come from?

As long as they drop in fairly soon after you (or if you have ridiculously large quantities of delta v) you can see the object outside before and after it falls in - it comes from the same patch of sky in my previous paragraph. If they wait too long you hit the singularity and die before seeing them fall in.

Curiously, at least in principle they will be able to see you after they fall in, however long they waited before following. In practice the light will rapidly red-shift into oblivion, so there's a practical time limit there too.