  We study gravitational perturbations in the Randall-Sundrum two-brane
background with scalar-curvature terms in the action for the branes, allowing
for positive as well as negative bulk gravitational constant. In the zero-mode
approximation, we derive the linearized gravitational equations, which have the
same form as in the original Randall-Sundrum model but with different
expressions for the effective physical constants. We develop a generic method
for finding tachyonic modes in the theory, which, in the model under
consideration, may exist only if the bulk gravitational constant is negative.
In this case, if both brane gravitational constants are nonzero, the theory
contains one or two tachyonic mass eigenvalues in the gravitational sector. If
one of the brane gravitational constants is set to zero, then either a single
tachyonic mass eigenvalue is present or tachyonic modes are totally absent
depending on the relation between the nonzero brane gravitational constant and
brane separation. In the case of negative bulk gravitational constant, the
massive gravitational modes have ghost-like character, while the massless
gravitational mode is not a ghost in the case where tachyons are absent.
