Schwartsschild from Newton + Relativity

  • Context: Graduate 
  • Thread starter Thread starter selfAdjoint
  • Start date Start date
  • Tags Tags
    Newton Relativity
Click For Summary

Discussion Overview

The discussion centers on the derivation of the Schwarzschild solution from Newtonian gravity and special relativity, as well as the implications of the Schwarzschild limit and escape velocity in the context of black holes. Participants explore theoretical interpretations and challenge each other's reasoning regarding the nature of the event horizon.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Matt Visser's derivation of the Schwarzschild solution is referenced as an interesting approach combining Newtonian gravity and special relativity.
  • One participant emphasizes that the Schwarzschild limit represents the point where escape velocity equals the speed of light, arguing it is not a physical barrier.
  • Another participant questions the necessity of defining the event horizon as a "wall," expressing confusion about the original point being made.
  • A repeated assertion suggests that if the Schwarzschild limit is not a wall, then objects should be able to escape, especially if they can achieve orbits at lower speeds.
  • Another participant counters that the Schwarzschild radius is defined as the boundary from which nothing can escape, indicating that general relativity is necessary to understand this concept fully.
  • There is a mention of the coincidence between Newtonian calculations of escape velocity and the Schwarzschild radius, suggesting that this relationship is not straightforward.
  • A participant expresses frustration with off-topic arguments and emphasizes the importance of adhering to the thread's original focus, while also noting the forum's guidelines regarding discussions of relativity.

Areas of Agreement / Disagreement

Participants do not reach consensus on the nature of the Schwarzschild limit and the implications of escape velocity. Multiple competing views remain regarding the interpretation of the event horizon and the relationship between Newtonian physics and general relativity.

Contextual Notes

Some arguments rely on assumptions about the definitions of escape velocity and the event horizon, which may not be universally accepted. The discussion also highlights the complexity of relating classical and relativistic physics without resolving the underlying mathematical principles.

selfAdjoint
Staff Emeritus
Gold Member
Dearly Missed
Messages
6,843
Reaction score
11
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.
 
Physics news on Phys.org
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.
 
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)
 
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."
 
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
 
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.
 
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.
 

Similar threads

  • · Replies 22 ·
Replies
22
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 53 ·
2
Replies
53
Views
6K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 22 ·
Replies
22
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 14 ·
Replies
14
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K