  We address the linear stability of a discontinuous surface of a relativistic
flow in the context of a jet that oscillates radially as it propagates. The
restoring force of the oscillation is expected to drive a Rayleigh-Taylor
instability (RTI) at the interface between the jet and its cocoon. We perform a
linear analysis and numerical simulations of the growth of the RTI in the
transverse plane to the jet flow with a uniform acceleration. In this system,
an inertia force due to the uniform acceleration acts as the restoring force
for the oscillation. We find that not only the difference in the inertia
between the two fluids separated by the interface but also the pressure at the
interface helps to drive the RTI because of a difference in the Lorenz factor
across the discontinuous surface of the jet. The dispersion relation indicates
that the linear growth rate of each mode becomes maximum when the Lorentz
factor of the jet is much larger than that of the cocoon and the pressure at
the jet interface is relativistic. By comparing the linear growth rates of the
RTI in the analytical model and the numerical simulations, the validity of our
analytically derived dispersion relation for the relativistic RTI is confirmed.
