Chaos in a modified Hénon–Heiles system describing geodesics in gravitational waves

Abstract

A Hamiltonian system with a modified Hénon–Heiles potential is investigated. This describes the motion of free test particles in vacuum gravitational pp-wave spacetimes with both quadratic (`homogeneous') and cubic (`non-homogeneous') terms in the structural function. It is shown that, for energies above a certain value, the motion is chaotic in the sense that the boundaries separating the basins of possible escapes become fractal. Similarities and differences with the standard Hénon–Heiles and the monkey saddle systems are discussed. The box-counting dimension of the basin boundaries is also calculated.