What does the Penrose diagram of a super extremal black hole (naked singularity) looks like? What does the Penrose diagram of a super extremal black hole (naked singularity) looks like?
I have seen the ones for regular charged/rotating black holes, but I can't find a good clear one for super extremal black holes.
 A: A good reference on how to draw Penrose diagrams is Walker's Block Diagrams and the Extension of Timelike Two‐Surfaces, J. Math. Phys. 11, 2280 (1970). It describes how to obtain block diagrams for metrics simple enough that one can write them in the form
$$\mathrm{d}s^2 = - F(r) \mathrm{d}t^2 + \frac{\mathrm{d}r^2}{F(r)},$$
while ignoring two dimensions (which is allowed due to some symmetry in the spacetime, such as spherical symmetry, or by choosing some particular slice of the spacetime). By generalizing the standard Kruskal extension construction that is done for Schwarzschild spacetime, one can treat way more general spacetimes by simply checking the zeros of $F(r)$ (assuming also that is is "well-behaved"). The trick is that this metric has a Killing vector field given by $\frac{\partial}{\partial t}$, and this field becomes null precisely at the points in which $F(r)$ vanishes. Hence, these are the null surfaces that "divide the blocks" in Penrose diagrams. By checking each of the zeroes, one can build each block and afterwards glue them together.
For a standard Schwarzschild black hole, one has
$$F(r) = 1 - \frac{2M}{r}.$$
This function has a zero at $r = 2M$ and a singularity at $r = 0$. This leads to a block corresponding to the region with $2M < r < +\infty$ and a different block for the region $0 < r < 2M$. Gluing them together in the most general way compatible with the time-orientation of each block, one obtains the Penrose diagram for Schwarzschild.
In a super-extremal case, we have the same function, but now the coordinate singularity $r = 2M$ happens for $r < 0$. Hence, we get a block for $0 < r < +\infty$. There's no longer a second block, because the coordinates $2M < r < 0$ can't really exist past the physical singularity at $r$ (it's been some time since I read Walker's paper, so I don't recall whether he gives much detail into this issue, but I find it likely for this to be hidden in there somewhere). Hence, the only block we get is this one:

While I never worked out the cases for charged and/or spinning black holes, I trust the same process will work and I'm quite confident that it will yield the same diagram for a charged black hole (as Tim Rias mentioned in the comments, a Kerr black hole allows for the observer to pass through $r = 0$, so it will be more complicated), since a null surface before the singularity would be an event horizon. Walker's paper develops the diagrams for the sub-extremal charged and spinning black holes, in case it interest you.
