Meaning of $M$ in Schwarzschild metric

Question

In the Schwarzschild metric

$$ds^2 = - \left(1-\frac{2M}{r} \right) dt^2 + \frac{dr^2}{1-\frac{2M}{r} }+ r^2 d\Omega^2. $$

Is it safe to call $M$ the mass of the source of curvature? Or should I just say its the mass of the central object?

Answer 1

$M$ is a parameter of the metric. To identify it as a mass, we need to define what we mean by masses in GR.

For that we use the ADM formalism: Wiki: ADM mass

Answer 2

Schwarzschild metric was presented some where around 1916,(https://en.wikipedia.org/wiki/Schwarzschild_metric ) you can pretty much be sure that "mass"(M) was considered as "mass" at that time. It's just the mass of the black hole.