Title:  Hypocycloid motion in the Melvin magnetic universe

Speaker: Yen-Kheng Lim

Host: Taotao Fang

Time: 14:30, Wednesday, Dec. 16

Location: Physics Building 552

Abstract:

We study the relativistic motion of charged particles moving in a magnetised universe known as the Melvin spacetime. When the angular velocity vector is opposite to the direction of the magnetic field lines, it is possible that the trajectory forms sharp cusps. We show that in two different perturbative regimes, these trajectories coincide exactly with hypocycloids. The first regime corresponds to perturbed circular orbits, while the second is the weak field regime. In the latter case, we derive an exact relation between the charge of the particle and the number of cusps. Hypocycloids from the two regimes are connected within a family of general, deformed hypocycloids parametrised by the magnetic field strength.

Bio:

Dr. Lim Yen Kheng is an Associate Professor of Mathematics at Xiamen University Malaysia. He received his PhD from the National University of Singapore. His research interests include black holes, general relativity and gravitational systems in the context of holography and quantum gravity.

Related references:
[1] Y.-K. Lim, "Hypocycloid motion in the Melvin magnetic universe," Phys. Rev. D 101 (2020) 104031

[2] V. P. Frolov, and A. A. Shoom, "Motion of charged particles near a weakly magnetized Schwarzschild black hole", Phys. Rev. D 82 (2010) 084034

[3] G. Venezian, "Terrestrial brachistochrone", Am. J. Phys. 34 (1966) 701