Reissner-Nordström

Kerr

Kerr-Newman

Horizon

$r_h=\frac{GM}{c^2}\pm \sqrt{\frac{G^2{M}^2}{c^4}-r_Q^2}$

$r_h=\frac{GM}{c^2}\pm \sqrt{\frac{G^2{M}^2}{c^4}-a^2}$

$r_h=\frac{GM}{c^2}\pm \sqrt{\frac{G^2{M}^2}{c^4}-r_Q^2-a^2}$

Extremal solution

$r_Q=\frac{GM}{c^2}$

$a=\frac{GM}{c^2}$

$r_Q^2+a^2=\frac{G^2{M}^2}{c^4}$

Extremal solution horizon

$r_h=\frac{GM}{c^2}$

$r_h=\frac{GM}{c^2}$

$r_h=\frac{GM}{c^2}$

Escape velocity extremal solution

$v_e=\sqrt{\frac{2GM}{r}-\frac{G^2{M}^2}{c^2{r}^2}}$

$v_e=\sqrt{\frac{2GM}{r}-\frac{G^2{M}^2}{c^2{r}^2}}$

$v_e=\sqrt{\frac{2GM}{r}-\frac{G^2{M}^2}{c^2{r}^2}}$