  We introduce AREPO-RT, a novel radiation hydrodynamic (RHD) solver for the
unstructured moving-mesh code AREPO. Our method solves the moment-based
radiative transfer equations using the M1 closure relation. We achieve second
order convergence by using a slope limited linear spatial extrapolation and a
first order time prediction step to obtain the values of the primitive
variables on both sides of the cell interface. A Harten-Lax-Van Leer flux
function, suitably modified for moving meshes, is then used to solve the
Riemann problem at the interface. The implementation is fully conservative and
compatible with the individual timestepping scheme of AREPO. It incorporates
atomic Hydrogen (H) and Helium (He) thermochemistry, which is used to couple
the ultra-violet (UV) radiation field to the gas. Additionally, infrared
radiation is coupled to the gas under the assumption of local thermodynamic
equilibrium between the gas and the dust. We successfully apply our code to a
large number of test problems, including applications such as the expansion of
${\rm H_{II}}$ regions, radiation pressure driven outflows and the levitation
of optically thick layer of gas by trapped IR radiation. The new implementation
is suitable for studying various important astrophysical phenomena, such as the
effect of radiative feedback in driving galactic scale outflows, radiation
driven dusty winds in high redshift quasars, or simulating the reionisation
history of the Universe in a self consistent manner.
