Relativistic radiation hydrodynamic equations in cylindrical coordinates

In many astrophysical systems such as accretion disks and jets, radiation interacts with relativistically moving matter. With applications to such systems in mind, I use the covariant tensor conservation laws to derive special relativistic, time-dependent, three-dimensional energy and momentum equations for matter and radiation in cylindrical coordinates. The equations can be conveniently applied to various radiation hydrodynamic processes with cylindrical symmetry. Radiation moments, like the radiation energy density, flux, and pressure, are defined in the comoving (with the flow) frame first and then transformed to the corresponding covariant quantities. The interaction between matter and radiation is also described in the comoving frame while the equations are represented in coordinates that are fixed with respect to the central object. As a concrete example, the relativistic equations of motion for a cylindrical gas flow interacting with a spherically symmetric radiation field are presented.