Length contraction compression and Schwarzschild radius

In summary, the conversation discusses the possibility of a rod moving fast enough to compress within its own Schwarzschild radius and whether it would collapse into a black hole. It is argued that the Schwarzschild solution, which assumes a stationary mass, is not applicable to a moving mass and that any simplifying assumptions in equations must be correct for the solution to hold. Additionally, it is noted that the concept of movement is relative in relativity and that the components of the metric tensor do not change with time in the Schwarzschild solution, making it unsuitable for describing a moving mass. Finally, the application of relativity of motion to a test particle falling towards a black hole is questioned.
  • #1
Ookke
172
0
We could imagine a rod moving fast enough to compress it within its own Schwarzschild radius. Should it collapse into a black hole? Or is the rod's own reference frame, where it isn't compressed, the one that makes decisions here?
 
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  • #2
Ookke said:
We could imagine a rod moving fast enough to compress it within its own Schwarzschild radius. Should it collapse into a black hole? Or is the rod's own reference frame, where it isn't compressed, the one that makes decisions here?
It doesn't collapse to a black hole in any reference frame. The Swarzschild solution is for a stationary mass. If you want to predict the behavior of a moving spherical mass you will have to derive a different solution, and that solution will surely tell you it doesn't form an event horizon.
 
  • #3
DaleSpam said:
If you want to predict the behavior of a moving spherical mass you will have to derive a different solution
:confused:

All movement is relative in relativity. What do you think is the difference between a moving and stationary mass in GR?
 
  • #4
MeJennifer said:
What do you think is the difference between a moving and stationary mass in GR?
A different form of the metric.

This issue has nothing to do with GR specifically. Anytime you make any simplifying assumption in order to solve an equation then the applicability depends on the correctness of the assumptions. If any assumption is significantly violated then the solution does not apply in that case.

One of the assumptions in the Schwarzschild solution is that the mass is stationary. Therefore you cannot use the Schwarzschild solution to argue that a relativistically moving mass collapses to a black hole. The assumptions are violated so the solution does not hold.
 
  • #5
DaleSpam said:
One of the assumptions in the Schwarzschild solution is that the mass is stationary.
That is just nonsense as the Schwarzschild solution is a vacuum solution. Feel free to write down here in this forum what metric describes a moving mass.

Also each mass in the universe is as stationary as any other mass, it is one of the first principles of relativity.
 
  • #6
MeJennifer said:
That is just nonsense as the Schwarzschild solution is a vacuum solution. Feel free to write down here in this forum what metric describes a moving mass.

Also each mass in the universe is as stationary as any other mass, it is one of the first principles of relativity.
I'm sorry this is confusing to you, but nothing you say here has any relevance and my GR background is not solid enough to explain this well. But I will try anyway.

The Schwarzschild metric assumes that the spacetime is spherically symmetric and stationary. The spacetime around a moving mass is neither spherically symmetric nor stationary.

Think of the ridiculous implications of using the Schwarzschild metric to describe a moving mass. A photon would orbit the photon sphere and keep on orbiting there even after the mass has moved far away. Even worse, the event horizon would not follow the mass. It is patently absurd.
 
  • #7
You are the one who is confused as you do not seem to understand that movement is relative.
 
  • #8
MeJennifer said:
You are the one who is confused as you do not seem to understand that movement is relative.
So ?
 
  • #9
In the Schwarzschild solution "t" is not an independent variable, so the components of the metric tensor do not change with the passage of time. Yet we would expect the gravitational field around us to change as a massive object moves by us. This is why it doesn't make sense to apply the Schwarzschild solution to the gravitational field around an object that is in motion relative to us.
 
  • #10
It is possible to write down the worldline for a test particle falling (accelerating) towards a black hole. Is it correct to apply the idea of relativity of motion here ? Can we say that this is the same scenario as a black-hole accelerating towards a test particle ?

I doubt it.
 
  • #11
Valid solutions in GR obviously use rest mass not relativistic mass as such solutions are observer independent.
 

1. What is length contraction and how does it relate to Einstein's theory of relativity?

Length contraction is the phenomenon where an object's length appears to decrease when it is moving at high speeds. This is a consequence of Einstein's theory of relativity, which states that time and space are relative and can change depending on an observer's perspective.

2. How is length contraction different from regular compression?

Length contraction is different from regular compression in that it occurs only when an object is moving at high speeds close to the speed of light. Regular compression, on the other hand, can occur due to external forces acting on an object, such as gravity or pressure.

3. What is the formula for calculating length contraction?

The formula for calculating length contraction is L = L0/γ, where L is the contracted length, L0 is the original length, and γ is the Lorentz factor, which is equal to 1/√(1 - v2/c2), with v being the velocity of the object and c being the speed of light.

4. How does the Schwarzschild radius relate to length contraction?

The Schwarzschild radius is a concept in physics that describes the size at which an object's gravitational pull becomes so strong that even light cannot escape from it. This radius is directly related to length contraction because as an object's velocity increases, its mass also increases, and therefore its Schwarzschild radius decreases.

5. Can length contraction be observed in everyday life?

Length contraction is only noticeable at extremely high speeds, such as those close to the speed of light. In everyday life, the speeds at which we move are too slow for length contraction to be observed. However, it has been experimentally confirmed through particle accelerators and other high-speed experiments.

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