  This study shows that a relativistic Hall effect significantly changes the
properties of wave propagation by deriving a linear dispersion relation for
relativistic Hall magnetohydrodynamics (HMHD). Whereas, in non- relativistic
HMHD, the phase and group velocities of fast magnetosonic wave become
anisotropic with an increasing Hall effect, the relativistic Hall effect brings
upper bounds to the anisotropies. The Alfve\'en wave group velocity with strong
Hall effect also becomes less anisotropic than non-relativistic case. Moreover,
the group velocity surfaces of Alfv\'en and fast waves coalesce into a single
surface in the direction other than near perpendicular to the ambient magnetic
field. It is also remarkable that a characteristic scale length of the
relativistic HMHD depends on ion temperature, magnetic field strength, and
density while the non-relativistic HMHD scale length, i.e., ion skin depth,
depends only on density. The modified characteristic scale length increases as
the ion temperature increases and decreases as the magnetic field strength
increases.
