  We study the in-medium masses of the charmonium states $J/\psi$ and
$\eta_{c}$ in the nuclear medium using QCD sum rule approach. These mass
modifications arise due to modifications of the scalar and the twist-2 gluon
condensates in the hot hadronic matter. The scalar gluon condensate,
$<\frac{\alpha_{s}}{\pi} G^a_{\mu\nu} {G^a}^{\mu\nu}>$ and the twist-2
tensorial gluon operator, $<\frac{\alpha_{s}}{\pi} G^a_{\mu\sigma}
{{G^a}_\nu}^{\sigma}>$ in the nuclear medium are calculated from the medium
modification of a scalar dilaton field introduced to incorporate trace anomaly
of QCD within the chiral SU(3) model used in the present investigation. The
effects of isospin asymmetry, density and temperature of the nuclear medium on
the in-medium masses of the lowest charmonium states $J/\psi$ and $\eta_{c}$
mesons are investigated in the present work. The results of the present
investigation are compared with the existing results on the masses of these
states. The medium modifications of the masses of these charmonium states
($J/\psi$ and $\eta_c$) seem to be appreciable at high densities and should
modify the experimental observables arising from the compressed baryonic matter
produced in asymmetric heavy ion collision experiments at the future facility
of FAIR, GSI.
