  Alfv\'{e}n wave collisions are the primary building blocks of the
non-relativistic turbulence that permeates the heliosphere and low-to-moderate
energy astrophysical systems. However, many astrophysical systems such as
gamma-ray bursts, pulsar and magnetar magnetospheres, and active galactic
nuclei have relativistic flows or energy densities. To better understand these
high energy systems, we derive reduced relativistic MHD equations and employ
them to examine weak Alfv\'{e}nic turbulence, dominated by three-wave
interactions, in reduced relativistic magnetohydrodynamics, including the
force-free, infinitely magnetized limit. We compare both numerical and
analytical solutions to demonstrate that many of the findings from
non-relativistic weak turbulence are retained in the relativistic system. But,
an important distinction in the relativistic limit is the inapplicability of a
formally incompressible limit, i.e, there exists finite coupling to the
compressible fast mode regardless of the strength of the magnetic field. Since
fast modes can propagate across field lines, this mechanism provides a route
for energy to escape strongly magnetized systems, e.g., magnetar
magnetospheres. However, we find that the fast-Alfv\'{e}n coupling is
diminished in the limit of oblique propagation.
