Integrability of Myers-Perry conformal mechanics
Seminars
Seminar “MODERN MATHEMATICAL PHYSICS”
Date and Time: Friday, 23 March 2018, at 2:00 PM
Venue: Blokhintsev Hall (4th floor), Bogoliubov Laboratory of Theoretical Physics
Seminar topic: «Integrability of Myers-Perry conformal mechanics»
Speaker: Armen Nersessian (Yerevan Physics Institute, Armenia)
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. 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 when 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.