  In the present work we consider the introduction of PT-symmetric terms in the
context of classical Klein-Gordon field theories. We explore the implication of
such terms on the spectral stability of coherent structures, namely kinks. We
find that the conclusion critically depends on the location of the kink center
relative to the center of the PT-symmetric term. The main result is that if
these two points coincide, the kink's spectrum remains on the imaginary axis
and the wave is spectrally stable. If the kink is centered on the "lossy side"
of the medium, then it becomes stabilized. On the other hand, if it becomes
centered on the "gain side" of the medium, then it is destabilized. The
consequences of these two possibilities on the linearization (point and
essential) spectrum are discussed in some detail.
