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Paper IPM / Physic / 15131

School of Physics

Title:

On integrability of geodesics in near-horizon extremal geometries

Author(s):

1 .	H. Demirchian
2 .	A. Nersessian
3 .	S. Sadeghian
4 .	M.M. Sheikh-Jabbari

Status:

Preprint

Journal:

Year:

2018

Supported by:

IPM

Abstract:

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 []. 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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