  The propagation of emissions in the relativistic streaming pair plasmas of
pulsars and magnetars is studied within the framework of Gordon effective
metric theory, and the effect of vacuum polarization on the radiation spectra
is examined particularly. It is found that the electromagnetic and kinetic
effects of streaming magnetized plasmas and the vacuum polarization effect can
shift the radiation spectra of stars. The modification of redshifts of spectra
can reach the same magnitude as the gravitational redshift in particular cases.
Moreover, the redshifts induced by the media are anisotropic and associated
with wave modes. For the O-mode, the modification of redshifts is dependent on
the frequency of the radiation. For lower-frequency radiation, the modification
is dominated by the plasma effect, while for higher-frequency radiations, by
the vacuum polarization effect. For the X-mode, the modification is
non-dispersive and dominated by the vacuum polarization effect. The vacuum
polarization also has a significant effect on the redshifts of X-ray emissions
in magnetars.
