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 by Hakobyan et al. [Phys. Lett. B 772, 586 (2017).]. We find the general solution of the Hamilton-Jacobi equations for these systems and present explicit expressions for the Liouville integrals and 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 a 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.
Highlights
Any dynamical system, particle or field dynamics alike, is classically described by equations of motion and some boundary conditions for the field theory case
We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions
We consider a nearhorizon extremal vanishing horizon case which happens for Myers-Perry black holes in odd dimensions and show that geodesic equations on this geometry are separable and work out its integrals of motion
Summary
Particle or field dynamics alike, is classically described by equations of motion and some boundary conditions for the field theory case. Particle dynamics on the near-horizon extreme geometries possesses dynamical 0 þ 1 dimensional conformal symmetry, i.e. it defines a “conformal mechanics” [5,7,8] This allows one to reduce the problem to the study of systems depending on latitudinal and azimuthal coordinates and their conjugate momenta with the effective Hamiltonian being Casimir of conformal algebra. III we analyze generic causal curve, massive or massless geodesic, in the NHEMP background We show that this Hamiltonian system is separable in an ellipsoidal coordinate system, work out the constants of motion, and establish that the system is integrable. In Boyer-Lindquist coordinates NHEMP metric has the form ds
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