The apparent shape of a rotating charged black hole, closed photon orbits and the bifurcation set A₄

Andreas de Vries, published in: Classical and Quantum Gravity 17(1), 123-144 (2000), doi:10.1088/0264-9381/17/1/309

The apparent shapes of Kerr-Newman space-times with different angular momentums and electric charges are geometrically given by the intersection of the swallow tail, the catastrophe or bifurcation set A₄, with a certain parameter manifold:

If we plot these shapes, we in fact see the shadow of a black hole of mass M with angular momentum a and electric charge Q, see Fig.2.

For Kerr-Newman space-times violating the the cosmic censorship hypothesis and containing a naked singularity, the plot in Fig.3 reveals a window to the anti-world of negative radii r, which in essence looks exactly like our world but only with negative mass.

You can let interactively plot some black hole shadow curves for various roration and charge parameters visiting the website

http://www.math-it.org/Mathematik/Astronomie/schatten.html.