Purely General Relativistic Effects Can Suppress Astrophysical Chaos*

The emergence of chaos in a spacetime deviating from Kerr in the mass quadrupole is governed only by the presence of that parameter. Space time around sources with more complex multipole structure can show the emergence of high order rotationally-induced multipoles that leaves its own imprint in the gravitational field of the source. The role of the rotation in the generation of chaos in the geodesic motion is comprehensively analyzed. The novel characteristic discussed in this work is that starting from a chaotic static configuration, the purely relativistic effects are capable of rebuilding broken tori by the quadrupole deformation by increasing slightly the rotation parameter of the source. This makes difficult the distinction between an integrable background by means of the observation of the gravitational waves.