3D Kerr Black Hole Orbits

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When a rotating star collapses to become a black hole it continues spinning. The grey region, called the ergosphere, is where the hole's spin drags space in the direction of the hole's rotation so strongly that nothing can move counter to the spin. The black hole is spinning like a top, with the spin axis pointing upwards.


Experiment with the controls to explore possible orbits:

The "spin rate" is how fast the black hole is spinning.

The "radius" controls how far from the black hole the planet's orbit starts.

is the angular momentum of the planet around the spin axis. is a measure of how fast the planet is orbiting. More , and the planet escapes. Less , it is captured. Negative , it orbits clockwise instead of counterclockwise.

is the polar angle, initially. indicates how far above or below the equatorial symmetry plane the planet starts. is the initial polar angular momentum. It indicates how fast the planet is moving, up or down, initially.

Choose an orbit from the drop down list, then click "orbit preset".

Move the sliders to find nearby orbits.


Contributed by: David Saroff (March 2011)
Open content licensed under CC BY-NC-SA



Thanks to Janna Levin for criticism and suggestions. The Hamiltonian from which the equations of motion were derived is in appendix A of Levin and Perez-Giz, "A Periodic Table for Black Hole Orbits", arXiv:0802.0459.

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