Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On integrability of geodesics in near-horizon extremal geometries: Case
  of Myers-Perry black holes in arbitrary dimensions   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.

13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga