### The apparent shape of a rotating charged black hole, closed photon orbits
and the bifurcation set *A*_{4}

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
*A*_{4}, 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.