Kerr-Newman, second order differential equations of motion for a charged particle and photons. Animations by Simon Tyran, Vienna (Yukterez)This is the english version. Deutschsprachige Version auf kerr.newman.yukterez.net und Yukipedia.
Shadow of an extremal Kerr-Newman BH with a²+℧²=M², Angle of view: edge on. For other parameters see here. Raw material: Commons.
Zoom with overlayed ergoshphere and horizon surfaces. Comparison with an uncharged Kerr black hole: click here
Retrograde orbit of a charged particle (q=1) around a BH with spin & charge a=√¾ & ℧=⅓. v0 & i0: local initial velocity & inclination
Prograde orbit of a neutral testparticle around a spinning and electrically charged black hole with spin a=0.9 and charge ℧=0.4
Prograde orbit of a negatively charged testparticle around a spiining and positively charged black hole with the same parameters as above
Free fall of a neutral testparticle around a rotating and charged naked singularity with spin a=1.5 and electric charge ℧=0.4
Geodesic orbit around a naked Kerr Newman ringsingularity with the same spin and charge parameters as in the last example
Chaotic orbit of a positively charged particle (q=½) orbit around a spinning and positively charged naked ring singularity (a=¾, ℧=⅔)
Nonequatorial and retrograde photon orbit around a naked singularity spinning with a=0.9 and charged with ℧=0.9
Retrograde photon orbit around a naked singularity (a=0.99, ℧=0.99). Local equatorial inclination angle: -2.5rad=-143.23945°
Stationary photon orbit (E=0) around a ringsingularity (a=½, ℧=1). Except at r=1, θ=90° v framedrag is <c everywhere, therefore no ergospheres.
Equatorial retrograde photon orbit, singularity at r=0→R=√(r²+a²)=a=½. Ergoring (green) at r=1, turning points at r=0.8 and r=1.3484
Nonequatorial and retrograde photon orbit around a spinning (a=½) and charged (℧=½) black hole, constant Boyer Lindquist radius
Polar photon orbit around a spinning (a=0.5) and charged (℧=0.75) naked singularity, constant Boyer Lindquist radius
Retrograde photon orbit of the third kind insinde a spinning (a=0.75) and charged (℧=0.5) black hole, constant BL radius
Orbit of a negatively charged particle inside a positively charged Reissner Nordström black hole (also see Dokuchaev, Fig. 1)