Reissner-Nordström

The Reissner-Nordström metric is a class of spherically symmetric electrovacuum spacetimes parametrized by two characteristic lengths, the Schwarzschild radius $r_s$ and the length scale $r_Q$, or alternatively a mass $M$ and charge $Q$, with the relation

\begin{eqnarray} r_s &=& \frac{2GM}{c^2}\\ r_Q &=& \frac{Q^2 G}{4\pi \varepsilon_0 c^4} \end{eqnarray}

1. History

2. Topology

3. Metrics and coordinates

$$ds^2 = (1 - \frac{r_s}{r} + \frac{r_Q}{r}) dt^2 - (1 - \frac{r_s}{r} + \frac{r_Q}{r})^{-1} dr^2 - r^2 (d\theta^2 + \sin^2 \theta d\varphi^2)$$

4. Tensor quantities

5. Symmetries

$\partial_t$, $\partial_\theta$, $\partial_\varphi$

6. Stress-energy tensor

7. Curves

8. Equations

9. Causal structure

10. Asymptotic structure

11. Energy conditions

12. Limits and related spacetimes

In the limit $Q = 0$, it reduces to the Schwarzschild metric.

13. Misc.

Bibliography