We study the nonlinear decay of the fast magnetosonic into the Alfv\'en waves
in relativistic force-free magnetohydrodynamics. The work has been motivated by
models of pulsar radio emission and fast radio bursts (FRBs), in which the
emission is generated in neutron star magnetospheres at conditions when not
only the Larmor but also the plasma frequencies significantly exceed the
radiation frequency. The decay process places limits on the source luminosity
in these models. We estimated the decay rate and showed that the phase volume
of Alfv\'en waves available for the decay of an fms wave is infinite. Therefore
the energy of fms waves could be completely transferred to the small-scale
Alfv\'en waves not via a cascade, as in the Kolmogorov turbulence, but
directly. Our results explain the anomalously low radio efficiency of the Crab
pulsar and show that FRBs could not be produced well within magnetar
magnetospheres.Comment: ApJ, in pres