# Schwarzschild metric

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?

## Answers and Replies

Nugatory
Mentor
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.

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
Mentor
2020 Award
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.