  We adopt a two-moment formalism, together with a reference-metric approach,
to express the equations of relativistic radiation hydrodynamics in a form that
is well-suited for numerical implementations in curvilinear coordinates. We
illustrate the approach by employing a gray opacity in an optically thick
medium. As numerical demonstrations we present results for two test problems,
namely stationary, slab-symmetric solutions in flat spacetimes, including
shocks, and heated Oppenheimer-Snyder collapse to a black hole. For the latter,
we carefully analyze the transition from an initial transient to a
post-transient phase that is well described by an analytically-known diffusion
solution. We discuss the properties of the numerical solution when rendered in
moving-puncture coordinates.
