  We continue our exploration of the collective modes of an anisotropic quark
gluon plasma by extending our previous analysis to arbitrary Riemann sheets. We
demonstrate that in the presence of momentum-space anisotropies in the parton
distribution functions there are new relevant singularities on the neighboring
unphysical sheets. We then show that for sufficiently strong anisotropies that
these singularities move into the region of spacelike momentum and their effect
can extend down to the physical sheet. In order to demonstrate this explicitly
we consider the polarization tensor for gluons propagating parallel to the
anisotropy direction. We derive analytic expressions for the gluon structure
functions in this case and then analytically continue them to unphysical
Riemann sheets. Using the resulting analytic continuations we numerically
determine the position of the unphysical singularities. We then show that in
the limit of infinite contraction of the distribution function along the
anisotropy direction that the unphysical singularities move onto the physical
sheet and result in real spacelike modes at large momenta for all
"out-of-plane" angles of propagation.
