  We present a theoretical study of excitations formed by hybridization between
magnons and phonons - magnon-polarons - in antiferromagnets. We first outline a
general approach to determining which magnon and phonon modes can and cannot
hybridize in a system thereby addressing the qualitative questions concerning
magnon-polaron formation. As a specific and experimentally relevant case, we
study Nickel Oxide quantitatively and find perfect agreement with the
qualitative analysis, thereby highlighting the strength of the former. We find
that there are two distinct features of antiferromagnetic magnon-polarons which
differ from the ferromagnetic ones. First, hybridization between magnons and
the longitudinal phonon modes is expected in many cubic antiferromagnetic
structures. Second, we find that the very existence of certain hybridizations
can be controlled via an external magnetic field, an effect which comes in
addition to the ability to move the magnon modes relative to the phonons modes.
