  The linearized relativistic magnetohydrodynamic (RMHD) equations describing a
uniform axially magnetized cylindrical relativistic jet spine embedded in a
uniform axially magnetized relativistically moving sheath are derived. The
displacement current is retained in the equations so that effects associated
with Alfven wave propagation near light speed can be studied. A dispersion
relation for the normal modes is obtained. Analytical solutions for the normal
modes in the low and high frequency limits are found and a general stability
condition is determined. A trans-Alfvenic and even a super-Alfvenic
relativistic jet spine can be stable to velocity shear driven Kelvin-Helmholtz
modes. The resonance condition for maximum growth of the normal modes is
obtained in the kinetically and magnetically dominated regimes. Numerical
solution of the dispersion relation verifies the analytical solutions and is
used to study the regime of high sound and Alfven speeds.
