  Nonradial oscillations of relativistic neutron stars with a solid crust are
computed in the relativistic Cowling approximation, in which all metric
perturbations are ignored. For the modal analysis, we employ three-component
relativistic neutron star models with a solid crust, a fluid core, and a fluid
ocean. As a measure for the relativistic effects on the oscillation modes, we
calculate the relative frequency difference defined as
$\delta\sigma/\sigma\equiv(\sigma_{GR}-\sigma_N)/\sigma_{GR}$, where
$\sigma_{GR}$ and $\sigma_R$ are, respectively, the relativistic and the
Newtonian oscillation frequencies. The relative difference
$\delta\sigma/\sigma$ takes various values for different oscillation modes of
the neutron star model, and the value of $\delta\sigma/\sigma$ for a given mode
depends on the physical properties of the models. We find that
$|\delta\sigma/\sigma|$ is less than $\sim0.1$ for most of the oscillation
modes we calculate, although there are a few exceptions such as the fundamental
(nodeless) toroidal torsional modes in the crust, the surface gravity modes
confined in the surface ocean, and the core gravity modes trapped in the fluid
core. We also find that the modal properties, represented by the
eigenfunctions, are not strongly affected by introducing general relativity. It
is however shown that the mode characters of the two interfacial modes,
associated with the core/crust and crust/ocean interfaces, have been
interchanged between the two through an avoided crossing when we move from
Newtonian dynamics to general relativistic dynamics.
