Young stellar object observations suggest that some jets rotate in the
opposite direction with respect to their disk. In a recent study, Sauty et al.
(2012) have shown that this does not contradict the magnetocentrifugal
mechanism that is believed to launch such outflows. Signatures of motions
transverse to the jet axis and in opposite directions have recently been
measured in M87 (Meyer et al. 2013). One possible interpretation of this motion
is the one of counter rotating knots. Here, we extend our previous analytical
derivation of counter-rotation to relativistic jets, demonstrating that
counter-rotation can indeed take place under rather general conditions. We show
that both the magnetic field and a non-negligible enthalpy are necessary at the
origin of counter-rotating outflows, and that the effect is associated with a
transfer of energy flux from the matter to the electromagnetic field. This can
be realized in three cases : if a decreasing enthalpy causes an increase of the
Poynting flux, if the flow decelerates, or, if strong gradients of the magnetic
field are present. An illustration of the involved mechanism is given by an
example of relativistic MHD jet simulation.Comment: Accepted for publication in ApJ