The [Schwarzschild metric][1] (for a black hole with mass $M$)
already contains the gravitational constant $G$,
when spelling out the Schwarzschild radius $r_s=\frac{2GM}{c^2}$:
$$\begin{align}
ds^2 &= \left(1-\frac{2GM}{c^2r}\right)c^2dt^2
 -\left(1-\frac{2GM}{c^2r}\right)^{-1}dr^2 \\
 &-r^2d\theta^2-r^2\sin^2\theta\ d\phi^2
\end{align}$$

And in a similar way the [Reissner-Nordström metric][2]
(for a black hole with mass $M$ and charge $Q$)
already contains the gravitational constant $G$
and the electric constant $\epsilon_0$:
$$\begin{align}
ds^2 &= \left(1-\frac{2GM}{c^2r}+\frac{GQ^2}{4\pi\epsilon_0c^4r^2}\right)c^2dt^2
 -\left(1-\frac{2GM}{c^2r}+\frac{GQ^2}{4\pi\epsilon_0c^4r^2}\right)^{-1}dr^2 \\
 &-r^2d\theta^2-r^2\sin^2\theta\ d\phi^2
\end{align}$$

 [1]: https://en.wikipedia.org/wiki/Schwarzschild_metric
 [2]: https://en.wikipedia.org/wiki/Reissner%E2%80%93Nordstr%C3%B6m_metric