Length contraction compression and Schwarzschild radius

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Discussion Overview

The discussion revolves around the implications of length contraction and the Schwarzschild radius in the context of a moving rod. Participants explore whether a rod moving fast enough to compress within its own Schwarzschild radius would collapse into a black hole, and the relevance of reference frames in this scenario.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants propose that a rod moving fast enough to compress within its own Schwarzschild radius should collapse into a black hole, while others argue that it does not collapse in any reference frame.
  • One participant states that the Schwarzschild solution is applicable only to stationary masses and suggests that a different solution is needed for moving spherical masses.
  • Another participant questions the distinction between moving and stationary masses in General Relativity (GR), suggesting that all movement is relative.
  • Some participants assert that the assumptions of the Schwarzschild solution, which include the mass being stationary, are violated when considering a moving mass, thus rendering the solution inapplicable.
  • There is a contention regarding the nature of the Schwarzschild solution as a vacuum solution and its implications for describing moving masses.
  • One participant highlights that the Schwarzschild metric assumes spherically symmetric and stationary spacetime, which does not hold for a moving mass.
  • Another participant discusses the implications of applying the Schwarzschild metric to a moving mass, suggesting it leads to absurd conclusions about the behavior of photons and event horizons.
  • There is a mention of the worldline for a test particle falling towards a black hole and a question about the applicability of the relativity of motion in this context.
  • One participant emphasizes that valid solutions in GR use rest mass rather than relativistic mass, as these solutions are observer independent.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the application of the Schwarzschild solution to moving masses, and the discussion remains unresolved with no consensus reached.

Contextual Notes

Participants highlight limitations related to the assumptions of the Schwarzschild solution and the applicability of different metrics for moving masses, but do not resolve these issues.

Ookke
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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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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.
 
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?
 
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.
 
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.
 
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.
 
You are the one who is confused as you do not seem to understand that movement is relative.
 
MeJennifer said:
You are the one who is confused as you do not seem to understand that movement is relative.
So ?
 
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.
 

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