Addendum: Chaos around a Hénon-Heiles-Inspired Exact Perturbation of a Black Hole

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We find that the model of a black hole plus an exterior halo of quadrupoles and octopoles recently proposed by us is more chaotic than previously detected. In fact, the quadrupolar component gives rise also to a chaotic behavior, found after further numerical search. This fact reinforces even more the role of chaos in relativistic core--halo models.