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Paper
IPM / Physic / 15131 |
School of Physics
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Title: |
On integrability of geodesics in near-horizon extremal geometries
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Author(s): |
| 1 . |
H. Demirchian
| | 2 . |
A. Nersessian
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S. Sadeghian
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M.M. Sheikh-Jabbari
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Status: |
Published
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Journal: |
Phys. Rev. D
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No.: |
10
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Vol.: |
97
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Year: |
2018
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Pages: |
104004
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Supported by: |
IPM
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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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