The Reissner-Nordstrom metric (in spherical coordinates and c = 1) differs from the Schwarzschild metric in a additive term $$\frac{GQ^2}{4\pi\epsilon_0 r^2}$$, so the metric is

$$ds^2 = \left(1 - \frac{2GM}{r} + \frac{GQ^2}{4\pi\epsilon_0 r^2}\right)dt^2 - \left(1 - \frac{2GM}{r} + \frac{GQ^2}{4\pi\epsilon_0 r^2}\right)^{-1} dr^2 - r^2d\Omega^2$$

This has an effect of "repulsion".

Why adding more energy (by the addition of charge to the black hole) has this repulsive effect? What is the physical meaning of adding charge to a black hole?