Chaotic motion around black holes

 

Motion of test particles around black holes surrounded by massive thin disc or ring could be chaotic for some parameters, which could be revealed by the value of the Lyapunov-like indicator MEGNO (mean exponential growth factor of nearby orbits). In the next two animations you can see the map of the phase space (r-v_r) of test particle moving around static black hole with mass 1M surrounded by the disc with inner rim placed at b=20M.Click on the picture to play the movie (author: Petra Sukova).In the first animation the mass of the disc is equal to 1.3 M and the energy of the particle is gradually growing.In the second animation the energy is constant (E=0.947) and the mass of the disc is changing.The higher the value of MEGNO is, which is indicated by the color scale in the animation, the more chaotic the motion is.

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