Follow an object into a black hole

[Psnarf]

TL;DR Summary

Does spaghettification continue inside a black hole?

In Stephen Hawking's Brief History of Time, an astronaut is stretched head to toe by the gravitational gradient of a black hole. Let us replace the astronaut with a large object and follow it inside as it travels along a radial line toward the center. I assume the gradient increases with, say, the square of the distance?

The object gets stretched farther and farther apart until we have a line of atoms, then the atoms themselves are stretched apart. Each stream of subatomic particles follows a radial line toward the center that converges with other streams from the object. I imagine fusion would occur at some point, creating larger atoms that get stretched apart. Would there be a stream of quarks?

The Higgs bosons would add to the depth of the black hole's gravity well.What happens to the electrons? Can two electrons merge? Since they are formless particles, perhaps a larger charge field? Does everything get converted to photons? Since the radial dimension becomes time itself, are all of the formless particles merged to form a dimensionless mass? Can a string even vibrate under such enormous forces? Of course we can but wonder.

 

[Ibix]

Starting at the beginning, yes, tidal forces rise all the way to the singularity. For a sufficiently large black hole a human could survive crossing the event horizon, but they would be killed before reaching the singularity.

I don't think details of what would happen at subatomic levels are really worth considering. Our model of gravity is not expected to be accurate where curvature is significant on atomic scales, so I wouldn't trust any predictions even if I knew enough about quantum field theory in curved spacetime to make any.

Yes, the mass of anything falling in is added to the mass of the hole, less a small (really, really small for an infalling man) amount of gravitational radiation as the event horizon settles down.

 

[Psnarf]

Forget about the astronaut. What happens when two streams of fermions are forced to converge? Can two electrons or two quarks fuse together?
What if the object were a ball of iron? Would not iron fusion draw energy from the black hole?

 

[Ibix]

What happens when two streams of fermions are forced to converge?

Step 1: develop a working theory of quantum gravity.
Step 2: apply it to this situation.

As I said, at the scale where curvature is comparable to atomic size we don't expect our models of gravity to be accurate.

That said, no, this process could not "draw energy from the black hole" in any externally meaningful sense. All of the fusion products are still contained within the black hole, so there are no detectable consequences outside the hole.

 

[Psnarf]

Is there a theoretical model of what exists between the event horizon and the spacetime singularity?

 

[Ibix]

In general relativity yes - nothing. Everything that falls in carries on falling until it reaches the singularity, so there'd be bits and pieces falling into the hole, but no structure.

But the singularity is almost certainly not there in reality - something else is, but we don't have a theory of quantum gravity to know what it is. Exactly where general relativity deviates significantly from reality is a point of debate - opinions range from "just above the event horizon" to "close to the singularity". We don't have a definitive answer yet.

 

[Psnarf]

Thank you for your reply. I was wrong to think there was empty space beyond the event horizon. I understand that mass accelerated to the speed of light would behave much like the common description of the singularity, stationary, formless, with infinite mass. I was wrong to picture two iron atoms 4x10^-10 meters apart forming a billion-meter triangle with the center coming to less than the Planc distance apart, pulled not by gravity, but the radial dimension of time. Folks a lot smarter than me will eventually postulate a theory of quantum gravity that can be verified by repeatable experiments. I can but wait.

 

[Ibix]

I was wrong to think there was empty space beyond the event horizon.

No, that's correct. An isolated black hole is vacuum inside, barring the occasional infalling physicist.

I understand that mass accelerated to the speed of light would behave much like the common description of the singularity, stationary, formless, with infinite mass.

This makes no sense. Nothing is "accelerated to the speed of light" and the rest isn't an accurate description of a singularity. It certainly doesn't have infinite mass.

I was wrong to picture two iron atoms 4x10^-10 meters apart forming a billion-meter triangle with the center coming to less than the Planc distance apart, pulled not by gravity, but the radial dimension of time.

That is wrong, certainly.

 

[Psnarf]

I forgot about time vs. gravity. Time does not propagate at one second per second everywhere. I like the notion of collapse then exlode, that is, the center of a supermassive black hole is exploding outward, but one second near the center is a billion years outside the Schwartzchild radius. In a small black hole, could the cycle of collapse, explode, collapse,..., or bouncing mass explain pulsars?
My feeble understanding of Swartzchild's solution to Einstein's field equations:

$$ds^2 = - \left( 1 - \frac {2GM} {rc^2} \right) dt^2 + \frac {dr^2} { \left( 1 - \frac {2GM} {rc^2} \right)} + r^2d\Omega^2$$
If the radius = $$\frac {2GM} {c^2},$$ the first term is 0 and the second $$\frac 1 0 = \infty$$
Therefore, things get undefined, but an infinite gravity would pull in the entire universe, which is not the case as observation shows expansion, not contraction. So we need a different solution?

 

[PeroK]

I forgot about time vs. gravity. Time does not propagate at one second per second everywhere. I like the notion of collapse then exlode, that is, the center of a supermassive black hole is exploding outward, but one second near the center is a billion years outside the Schwartzchild radius. In a small black hole, could the cycle of collapse, explode, collapse,..., or bouncing mass explain pulsars?

Your last two posts are simply nonsense.

 

[Ibix]

Time does not propagate at one second per second everywhere.

Time does not propagate, full stop.

I like the notion of collapse then exlode, that is, the center of a supermassive black hole is exploding outward, but one second near the center is a billion years outside the Schwartzchild radius. In a small black hole, could the cycle of collapse, explode, collapse,..., or bouncing mass explain pulsars?

None of that makes any sense. Pulsars are fairly well understood phenomena, a form of rotating neutron star or white dwarf, and have nothing to do with black holes.

Therefore, things get undefined, but an infinite gravity would pull in the entire universe, which is not the case as observation shows expansion, not contraction. So we need a different solution?

The Schwarzschild coordinates are undefined at the event horizon, but other coordinates work just fine through the event horizon. The singularity is not the same as the event horizon.

If you want to learn relativity, you will need a proper source. Sean Carroll's lecture notes on GR are a good source, as is Ben Crowell's GR text, and both are free to download. You will need to know special relativity first, if you are not familiar with it. For that, I recommend Taylor and Wheeler's Spacetime Physics, which has recently been made available for download by the authors (but it's a scanned copy, so it's a large file).

 

[Nugatory]

I forgot about time vs. gravity. Time does not propagate at one second per second everywhere.

On the contrary, it does, and understanding how this can be despite time dilation and the twin paradox is essential to making sense of relativity. It's probably best to start with the flat spacetime of special relativity, where there are fewer counterintuitive pitfalls:
1) Understand relativity of simultaneity and how it ecplains the apparent paradox that when you and I are moving relative to one another we both find that we have the faster clock.
2) Understand the twin paradox. Many threads here, more than I'm going to link to now.

Until you are comfortable enough with these to explain them to someone else, you aren't ready to start in on curved spacetime, gravity, and general relativity. The good news is that it's not that hard, it's more a conceptual shift to a new way of thinking about things than any serious mathematical heavy lifting.

 

[Psnarf]

Thank you for being gentle to this retired systems analyst and lifelong learner. It's been over 40 years since I aced my 3-semester physics course. I'm starting over with Dr.Susskind's lectures from Stanford. First I have to forget everything I picked up reading physics-related twaddle published by idiots. The internet is a terrible thing.