The transfer equation for photons is obtained from the Lindquist formalism in curvilinear coordinates (no symmetry assumed), in an arbitrary frame and in any basis (natural or physical), to first order in O(v/c). Acceleration terms in the fluid are introduced via a modification of the metric tensor. The local tetrad attached to the accelerated fluid element follows a Fermi-Walker transport. Lorentz transformations are used to transform locally the equation from Lagrangian to Eulerian space-time coordinates. The resulting equation agrees in the case of a local Minkowskian space with the equation obtained directly using special-relativistic considerations.