  We calculate the in-medium $D$ and $\bar D$-meson masses in isospin
asymmetric nuclear matter in an effective chiral model. The $D$ and $\bar D$ -
mass modifications arising from their interactions with the nucleons and the
scalar mesons in the effective hadronic model are seen to be appreciable at
high densities and have a strong isospin dependence. These mass modifications
can open the channels of the decay of the charmonium states ($\Psi^\prime$,
$\chi_c$, $J/\Psi$) to $D \bar D$ pairs in the dense hadronic matter. The
isospin asymmetry in the doublet $D=(D^0,D^+)$ is seen to be particularly
appreciable at high densities and should show in observables like their
production and flow in asymmetric heavy ion collisions in the compressed
baryonic matter experiments in the future facility of FAIR, GSI. The results of
the present work are compared to calculations of the $D(\bar D$) in-medium
masses in the literature using the QCD sum rule approach, quark meson coupling
model, coupled channel approach as well as from the studies of quarkonium
dissociation using heavy quark potentials from lattice QCD at finite
temperatures.
