Chaotic Dynamics in a Superposed Weyl Spacetime

A general superposed solution between a Schwarzschild black hole and one of the first family of Lemos-Letelier disks with two opposite dipoles is given. For the Newtonian core-disk system, it is integrable in the region z > 0 or <0, but it might be nonintegrable over the global interval of z since the Newtonian potential from the disk has discontinuous derivatives. On the other hand, Poincaré sections reveal that the dynamics of test particles in the relativistic core-disk system depends on some specified dynamical parameters. The system goes from regular to chaotic with increasing disk parameter. In addition, other parameters such as energy and angular momentum have an impact on chaos. The larger the energy gets, or the smaller the angular momentum becomes, the more dramatic chaos the system produces. If the interaction term between the black hole and the disk is dropped, chaos seems to die out. This fact illustrates sufficiently that the nonlinearity of the Einstein field equations is a crucial factor for the onset of chaos. Note, as a crucial point, that there is a much thinner chaotic domain trapped in a larger regular region in the case of larger angular momenta, unlike the case of smaller angular momenta. This can also be described by the spectral analysis and the invariant Lyapunov exponents.