The Schwarzschild Metric: Obtaining Equation M=Gm/c^2 & Newton Law at Infinity

[TimeRip496]

How do you obtain this equation M=Gm/c^2. What does M stand for? Is is Newton law at infinity? Again what is this Newton law at infinity?

 

[Nugatory]

How do you obtain this equation M=Gm/c^2. What does M stand for?

M is just the mass of the black hole using units in which G and c are both equal to one.

We don't have to make this substitution but if we don't we'll be schlepping factors of G and c around everywhere in our equations, and they're complicated enough already.

 

[TimeRip496]

M is just the mass of the black hole using units in which G and c are both equal to one.

We don't have to make this substitution but if we don't we'll be schlepping factors of G and c around everywhere in our equations, and they're complicated enough already.

Do you mind telling me a source for such derivation? Cause all the Internet gives is just the derivation of the schwarzschild radius.

 

[PeterDonis]

Do you mind telling me a source for such derivation?

It's just a conversion factor from mass units to length units; $Gm / c^2$ converts the mass $m$ to an equivalent length. The Schwarzschild radius corresponding to $m$ is just twice that equivalent length.