Schwartsschild from Newton + Relativity

In summary, Matt Visser has a neat derivation of the Schwartzschild solution of Einstein's equations from Newtonian gravity, the covariances of special relativity, and a plusible sounding heuristic.
  • #1
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Matt Visser has a neat derivation of the Schwartzschild solution of Einstein's equations from Newtonian gravity, the covariances of special relativity, and a plusible sounding heuristic.

http://arxiv.org/abs/gr-qc/0309072

Enjoy.
 
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  • #2
Has this ever occurred to anybody? The Schwarzschild limit is the spot that the escape velocity is light speed. It is not a wall. What escape velocity means is that if a body is not going that speed, it will not escape. It is not a wall.
 
  • #3
Nobody thinks it's a wall. What's your point? (I don't mean to be insulting, I just really do not understand what point you are trying to make with that post)
 
  • #4
DavidGTaylor said:
Has this ever occurred to anybody? The Schwarzschild limit is the spot that the escape velocity is light speed. It is not a wall. What escape velocity means is that if a body is not going that speed, it will not escape. It is not a wall.

I doubt that it has ever occurred to any competent relativist that the event horizon might be "a wall." Therefore it would never have occurred to them in a flash of blinding insight that it was "not a wall."
 
  • #5
Then if it is not a wall (something did think a little obvious) then why can't particles/objects/radiation not get out? An object could orbit a S.O. and pickup other items ejected from the S.O. at less than escape velocity (c) and take the items into permanent orbit. How could that not constitute escape? Especially when you take the scale big enough. An object could pass the border on a S.O. with the mass of the universe (the border being a point where gravity would be of the 1.0E-10m/s^2) achieving orbit at a spot 10 billion light years away, where the orbital speed would be c/4. How is that not escape. Wouldn't need Hawking leakage for that spot either
 
  • #6
I'm not sure I entirely understand your argument... but it seems like you're saying that objects can move to higher orbits even if they don't have escape velocity, so why is it that something in a black hole should be stuck there forever?

If I've understood correctly, you should know that the Schwarzschild radius - or technically, the radius of the event horizon - is defined as the boundary of the region which nothing can escape from. But you kind of need general relativity to tell you that.

It just happens that if you ignore relativity and, using pure Newtonian physics, calculate the radius at which the escape velocity is equal to c, you happen to get the formula for the Schwarzschild radius. It's a pure coincidence.
 
  • #7
DavidGTaylor said:
Then if it is not a wall (something did think a little obvious) then why can't particles/objects/radiation not get out?
See my post #35 here, the event horizon cannot be understood purely in terms of the classical notion of escape velocity. In any case this argument of yours is totally off-topic for this thread, please try to stick to discussing things directly related to the opening post of whatever thread you're on--if you want to a new thread to discuss some issue you're interested in, there's a "new topic" button on the upper left of the main page for the relativity forum. Also please note the IMPORTANT! Read before posting note, this forum is not a place to dispute the validity of relativity, although you can ask questions about things that don't make sense to you as long as you are open-minded about the idea that it would make sense if you understood the subject better.
 

1. What is the Schwartsschild metric in relation to Newtonian and Relativistic physics?

The Schwartsschild metric is a mathematical representation of the curvature of space-time around a non-rotating, spherically symmetric mass. It is derived from Einstein's theory of General Relativity and is used to describe the gravitational field of a massive object, such as a black hole. This metric is an improvement upon Newton's law of gravitation, which does not account for the effects of space-time curvature.

2. How does the Schwartsschild metric differ from Newton's law of gravitation?

Newton's law of gravitation is a classical theory that describes the attractive force between two objects with mass. It is based on the concept of a gravitational force acting at a distance. In contrast, the Schwartsschild metric is a relativistic theory that describes gravity as the curvature of space-time caused by the presence of mass. It takes into account the effects of space-time curvature and the speed of light, which Newton's law does not.

3. Can the Schwartsschild metric be used to explain the phenomenon of black holes?

Yes, the Schwartsschild metric is a fundamental tool in understanding and describing the properties of black holes. It predicts the existence of an event horizon, which is the point of no return for anything crossing it, including light. This metric also explains other phenomena associated with black holes, such as gravitational lensing and time dilation.

4. How does the Schwartsschild metric affect our understanding of the universe?

The Schwartsschild metric is an essential component of the General Theory of Relativity, which is the current model for understanding gravity and the structure of the universe. Its predictions have been confirmed through various observations, such as the bending of light near massive objects and the redshift of light from distant galaxies. It has also led to the discovery of other phenomena, such as gravitational waves.

5. Are there any limitations to the Schwartsschild metric?

Like any scientific theory, the Schwartsschild metric has its limitations. It is a classical theory and does not take into account the principles of quantum mechanics, which are necessary for understanding the behavior of matter and energy at the smallest scales. Additionally, it does not account for the effects of other forces, such as electromagnetism, which are also important in our understanding of the universe.

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