  The rising amount of polarized observations of relativistic sources requires
the correct theory for proper model fitting. The equations for general
relativistic (GR) polarized radiative transfer are derived starting from the
Boltzmann equation and basic ideas of general relativity. The derivation is
aimed at providing a practical guide to reproducing the synchrotron part of
radio & sub-mm emission from low luminosity active galactic nuclei (LLAGNs), in
particular Sgr A*, and jets. The recipe for fast exact calculation of
cyclo-synchrotron emissivities, absorptivities, Faraday rotation and conversion
coefficients is given for isotropic particle distributions. The multitude of
physical effects influencing simulated spectrum is discussed. The application
of the prescribed technique is necessary to determine the black hole (BH) spin
in LLAGNs, constraining it with all observations of total flux, linear and
circular polarization fractions, and electric vector position angle as
functions of the observed frequency.
