I have been dealing with the following issue related to the Schwarzschild geometry recently. When expressed as: $$ ds^{2}=-\left(1-\frac{2GM}{r}\right)dt^{2}+\frac{1}{1-\frac{2GM}{r}}dr^{2}+d\Omega_{2}^{2}$$ one can find a Killing vector $\xi=\partial_{t}$, since there are no components of the me...