The Schwarzschild metric (for a black hole with mass $M$) already contains the gravitational constant $G$, when spelling out the Schwarzschild radius $r_s=\frac{2GM}{c^2}$: $$\begin{align} ds^2 &= \left(1-\frac{2GM}{c^2r}\right)c^2dt^2 -\left(1-\frac{2GM}{c^2r}\right)^{-1}dr^2 \\ &-r^2d\theta^2-r^2\sin^2\theta\ d\phi^2 \end{align}$$$$\begin{align} ds^2 &= \left(1-\frac{2GM}{c^2r}\right)c^2dt^2 \\ &-\left(1-\frac{2GM}{c^2r}\right)^{-1}dr^2 \\ &-r^2d\theta^2-r^2\sin^2\theta\ d\phi^2 \end{align}$$
And in a similar way the Reissner-Nordström metric (for a black hole with mass $M$ and charge $Q$) already contains the gravitational constant $G$ and the electric constant $\epsilon_0$: $$\begin{align} ds^2 &= \left(1-\frac{2GM}{c^2r}+\frac{GQ^2}{4\pi\epsilon_0c^4r^2}\right)c^2dt^2 -\left(1-\frac{2GM}{c^2r}+\frac{GQ^2}{4\pi\epsilon_0c^4r^2}\right)^{-1}dr^2 \\ &-r^2d\theta^2-r^2\sin^2\theta\ d\phi^2 \end{align}$$$$\begin{align} ds^2 &= \left(1-\frac{2GM}{c^2r}+\frac{GQ^2} {4\pi\epsilon_0c^4r^2}\right)c^2dt^2 \\ &-\left(1-\frac{2GM}{c^2r}+\frac{GQ^2}{4\pi\epsilon_0c^4r^2}\right)^{-1}dr^2 \\ &-r^2d\theta^2-r^2\sin^2\theta\ d\phi^2 \end{align}$$
For a black brane you can do it in the same way by spelling out the Schwarzschild radius $r_s$.