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


Figure 2. The apparent shadow shapes of different black holes as seen by a distant observer, if the black hole is apparently in front of a source of illumination with an angular size larger than that of the black hole. Proceeding each row of the matrix means increasing charge Q, going down each column yields increasing angular momentum a.

The south-west to north-east diagonal represents the extreme cases a2 + Q2=M2. Below this diagonal we have the cases a2+Q2>M2 which do not satisfy the cosmic censorship hypothesis, i.e. where there does not exist an event horizon and a naked singularity is present. Moreover, there are no direct circular photon orbits, only retrograde null geodesics may be circular. in this way the asymptotic observer does not see a closed black area but merely a bright open arc.

We notice that increasing angular momentum at constant charge augments the area of the apparent black shape, whereas increasing absolute value of charge at constant angular momentum diminishes it.