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

• TimeRip496
In summary, the equation M=Gm/c^2 is used to determine the mass of a black hole in units where G and c are equal to one. M stands for the mass of the black hole, and it is a conversion factor from mass units to length units. The Schwarzschild radius is equal to twice the equivalent length determined by this equation. The derivation of this equation can be found by searching online for the Schwarzschild radius.

#### 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?

TimeRip496 said:
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.

Nugatory said:
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.

TimeRip496 said:
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.