The apparent shape of a rotating charged black hole, closed photon orbits and the bifurcation set A 4

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Abstract
The apparent shapes of various Kerr-Newman spacetimes are plotted. For this purpose the geometry of closed photon orbits is studied, forming a subset of the bifurcation set A 4 , well known in elementary catastrophe theory. One additional result is that the cosmic censorship hypothesis guarantees that the spacetime casts a shadow, whereas naked ring singularities enable the visibility of the `anti-world' of negative radii r through its interior. Moreover, the optical restrictions to the observability of the shadow of an astronomical black hole are inferred.