Publication at Faculty of Mathematics and Physics |
2019
Abstract
We study the dynamics of time-like geodesics in the field of black holes perturbed by a circular ring or disc, restricting to static and axisymmetric class of space-times. The focus is in particular on the transition to chaos when the integrability of the system is broken by a small perturbation.
To determine whether the resulting dynamics is chaotic or not we employ the Melnikov method which detects the chaotic layer arising by break-up of a homoclinic orbit. The conclusions of this analytical method will then be confronted with numerical results.