Feat: Kerr-Newman metric

[fjebaker]

The event horizon is not being correctly calculated for this metric yet, suggesting there is a typo somewhere but I can't seem to find it.

There's also the ambiguity between the EH being

$$ \left. \frac{1}{g{rr}}\right \rvert{r_\text{EH}} = 0, $$

or the Killing horizon corresponding to the $\frac{\partial}{\partial t}$ and $\frac{\partial}{\partial \phi}$ Killing vectors, i.e.

$$ \left. \left( g{t\phi}^2 - g{tt} g{\phi \phi} \right) \right\rvert{r_\text{EH}} = 0. $$

They should be the same. For the Kerr-Newman metric currently implemented, they are not when $|a|>0$.. so... that needs to be fixed.

Also missing tests.

[fjebaker]

Found the mistake! Once again, I had a factor $2$ too much in the $g_{t\phi}$ component.

[fjebaker]

From Ghosh & Afrin (2023):

For the case of $Q = 0$ and $Q = 0.6$ with our code:

[fjebaker]

Just to be a bit cheeky, setting the integration domain to terminate further from the event horizon (above figure is to within $1$% of $r\text{g}$ or $\approx 1.0227 r\text{g}$, now setting $20$% of $r\text{g}$ or $\approx 1.215 r\text{g}$):

It's a little bit rounder (~;

Overlaying the closer approximation, since this only affects the left side: