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On integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions
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We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is integrable and separable, extending the results of the odd dimensional case discussed in arXiv:1703.00713. We find the general solution of the Hamilton-Jacobi equations for these systems and present explicit expressions for the Liouville integrals, discuss Killing tensors and the associated constants of motion. We analyze special cases of the background near-horizon geometry were the system possesses more constants of motion and is hence superintegrable. Finally, we consider near-horizon extremal vanishing horizon case which happens for Myers-Perry black holes in odd dimensions and show that geodesic equations on this geometry are also separable and work out its integrals of motion.
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Integrable systems connected with black holes
The thesis derives explicit first integrals and Killing tensors for geodesics in near-horizon Myers-Perry black holes, introduces a B-memory formulation of gravitational memory, and constructs resonant spacetimes from...
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