# B Schwarzschild radius

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1. Nov 25, 2016

### stoomart

Learning about Schwarzschild radius from Wikipedia:
Is it accurate to say any object of mass crossing the event horizon of a black hole is compressed sufficiently to have its own Schwarzschild radius, becoming a black hole itside of a black hole?

2. Nov 25, 2016

### Staff: Mentor

No. For a super massive black hole nothing particularly bad happens at the event horizon in standard GR.

3. Nov 25, 2016

### stoomart

Is there a known equation to calculate the gravitational or external force required to compress an object to the volume of its Schwatzchild radius?

4. Nov 25, 2016

### Staff: Mentor

No. (This is true even if we leave out the rest of the sentence.)

You can't; before you reach that point, the object's internal structure will be destroyed and it will collapse. The limit before that happens is actually 9/8 of the Schwarzschild radius; at that point, even infinite internal pressure is insufficient to keep the object static.

Also, asking what force is required to achieve this is a bit misleading, because there is no way to exert force without a source of energy, and that energy will itself gravitate and contribute to the total mass of the system. So if, for example, we rig up a big piston and use it to start pushing an object together, we will find that what eventually becomes a black hole if things get compact enough is not just the object inside the piston, but the whole assembly of object, piston, and the piston's energy source.

5. Nov 25, 2016

### stoomart

I had two scenarios in mind: near/at the singularity in a common black hole, and inside a particle accelerator.

6. Nov 25, 2016

### Staff: Mentor

Here the matter is already inside a black hole, so it already is compressed enough to form a black hole. Compressing it more makes no difference.

We are still many orders of magnitude away from being able to probe the Planck regime in particle accelerators, which is what it would take to have a significant chance of making a black hole inside of one.

7. Nov 25, 2016

### stoomart

So then a foreign object entering a black hole does get compressed to/past its Schwartzchild radius? I interpreted Dale's response as saying this doesn't happen.

8. Nov 25, 2016

### Staff: Mentor

You do realize that the event horizon and the singularity are entirely different, right? I was answering a question about the event horizon, and @PeterDonis was answering a question about the singularity.

Again, for a sufficiently large black hole nothing happens to an object crossing the event horizon. At the singularity our theories break down, but long before that tidal forces would shred any matter.

9. Nov 25, 2016

### stoomart

Yes, maybe I was too vague (or wordy) in my OP. When I said "crossing the event horizon", I was referring generally to entering a black hole. Is it currently known where in a black hole matter is compressed?

10. Nov 25, 2016

### Staff: Mentor

Usually the word used is "spaghettified". It is compressed in the horizontal directions and stretched in the vertical direction. For a large black hole that would be close to the singularity. For a small black hole it could be well outside the event horizon.

That is for a test object free falling. For a static structure surrounding the black hole, see @PeterDonis answer above.

11. Nov 26, 2016

### Staff: Mentor

No. See below.

As Dale said, what actually happens is compression horizontally and stretching vertically. (Actually, this is only true in a highly idealized black hole that formed from a perfectly spherically symmetrical collapsing object. In a real hole, the stretching/compressing would be highly chaotic--google "BKL singularity" if you want the gory details.)

However, as I said before, thinking of this process as eventually "compressing matter inside its Schwarzschild radius" (even along just one dimension) is not correct. The matter is already inside a black hole, so it is already inside its Schwarzschild radius. In other words, once a small object falls into a black hole, you can't really think of it as having a separate "Schwarzschild radius" of its own. It's part of the black hole in that respect, and its Schwarzchild radius is the same as that of the hole.

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