# Schwartsschild from Newton + Relativity

#### selfAdjoint

Staff Emeritus
Gold Member
Dearly Missed
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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#### DavidGTaylor

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.

#### diazona

Homework Helper
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)

#### bcrowell

Staff Emeritus
Science Advisor
Gold Member
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."

#### DavidGTaylor

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

#### diazona

Homework Helper
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.

#### JesseM

Science Advisor
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.

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