Schwarzschild Radius: Compression Inside Black Holes

In summary, the Schwarzschild radius is defined as the radius of a sphere in which all the mass of an object is compressed to the point where the escape velocity from the surface of the sphere equals the speed of light. Objects crossing the event horizon of a black hole are compressed in the horizontal direction and stretched vertically, with the degree of compression being greater for smaller black holes. However, once an object enters a black hole, it becomes part of the black hole and its own Schwarzschild radius is the same as that of the black hole.
  • #1
stoomart
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Learning about Schwarzschild radius from Wikipedia:
the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface of the sphere would equal the speed of light

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?
 
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  • #2
stoomart said:
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?
No. For a super massive black hole nothing particularly bad happens at the event horizon in standard GR.
 
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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
stoomart said:
Is it accurate to say any object of mass crossing the event horizon of a black hole is compressed

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

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

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
PeterDonis said:
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.
I had two scenarios in mind: near/at the singularity in a common black hole, and inside a particle accelerator.
 
  • #6
stoomart said:
near/at the singularity in a common black hole

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.

stoomart said:
inside a particle accelerator.

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

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
stoomart said:
Is it currently known where in a black hole matter is compressed?
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
stoomart said:
So then a foreign object entering a black hole does get compressed to/past its Schwartzchild radius?

No. See below.

stoomart said:
Is it currently known where in a black hole matter is compressed?

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 Schwarzschild radius is the same as that of the hole.
 
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FAQ: Schwarzschild Radius: Compression Inside Black Holes

What is the Schwarzschild radius?

The Schwarzschild radius is the boundary of a black hole, also known as the event horizon. It is the distance from the center of the black hole at which the escape velocity exceeds the speed of light, making it impossible for anything, including light, to escape from the black hole.

How is the Schwarzschild radius related to the mass of a black hole?

The Schwarzschild radius is directly proportional to the mass of a black hole. The larger the mass of a black hole, the larger its Schwarzschild radius will be. This means that the more massive a black hole is, the stronger its gravitational pull will be, making it even harder for anything to escape its event horizon.

What happens to matter as it approaches the Schwarzschild radius?

As matter approaches the Schwarzschild radius, the gravitational pull becomes stronger and stronger. This causes the matter to become compressed and squeezed, leading to extreme pressure and temperature. Eventually, the matter will reach a singularity, a point of infinite density and zero volume, at the center of the black hole.

How does the Schwarzschild radius affect time and space?

Inside the event horizon of a black hole, the gravitational pull is so strong that it warps both time and space. Time moves slower the closer you get to the Schwarzschild radius, and at the event horizon, time stands still. This also means that space is highly distorted, making it impossible to see anything beyond the event horizon.

Can anything escape from inside the Schwarzschild radius?

No, once anything crosses the event horizon and enters the Schwarzschild radius, it is impossible for it to escape. The gravitational pull is too strong, and the escape velocity exceeds the speed of light. This is why black holes are often described as "cosmic prisons" - anything that enters cannot escape.

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