Length contraction compression and Schwarzschild radius

[Ookke]

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?

 

[Dale]

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.

 

[MeJennifer]

If you want to predict the behavior of a moving spherical mass you will have to derive a different solution

All movement is relative in relativity. What do you think is the difference between a moving and stationary mass in GR?

 

[Dale]

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.

 

[MeJennifer]

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.

 

[Dale]

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.

 

[MeJennifer]

You are the one who is confused as you do not seem to understand that movement is relative.

 

[Dale]

You are the one who is confused as you do not seem to understand that movement is relative.

So ?

 

[snoopies622]

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.

 

[Mentz114]

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.

 

[MeJennifer]

Valid solutions in GR obviously use rest mass not relativistic mass as such solutions are observer independent.