  The excitation of solar and solar-like g modes in non-relativistic stars by
arbitrary external gravitational wave fields is studied starting from the full
field equations of general relativity. We develop a formalism that yields the
mean-square amplitudes and surface velocities of global normal modes excited in
such a way. The isotropic elastic sphere model of a star is adopted to
demonstrate this formalism and for calculative simplicity. It is shown that
gravitational waves solely couple to quadrupolar spheroidal eigenmodes and that
normal modes are only sensitive to the spherical component of the gravitational
waves having the same azimuthal order. The mean-square amplitudes in case of
stationary external gravitational waves are given by a simple expression, a
product of a factor depending on the resonant properties of the star and the
power spectral density of the gravitational waves' spherical accelerations.
Both mean-square amplitudes and surface velocities show a characteristic
R^8-dependence (effective R^2-dependence) on the radius of the star. This
finding increases the relevance of this excitation mechanism in case of stars
larger than the Sun.
