  We stress that halo dipole components are nontrivial in core-halo systems in
both Newton's gravity and General Relativity. To this end, we extend a recent
exact relativistic model to include also a halo dipole component. Next, we
consider orbits evolving in the inner vacuum between a monopolar core and a
pure halo dipole and find that, while the Newtonian dynamics is integrable, its
relativistic counterpart is chaotic. This shows that chaoticity due only to
halo dipoles is an intrinsic relativistic gravitational effect.
