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We construct a general relativistic radiative transfer (RT) formulation,applicable to particles with or without mass in astrophysical settings. Derivedfrom first principles, the formulation is manifestly covariant. Absorption andemission, as well as relativistic, geometrical and optical depth effects aretreated self-consistently. The RT formulation can handle 3D geometricalsettings and structured objects with variations and gradients in the opticaldepths across the objects and along the line-of-sight. The presence of masscauses the intensity variation along the particle bundle ray to be reduced byan aberration factor. We apply the formulation and demonstrate RT calculationsfor emission from accretion tori around rotating black holes, considering twocases: idealised optically thick tori that have a sharply defined emissionboundary surface, and structured tori that allow variations in the absorptioncoefficient and emissivity within the tori. Intensity images and emissionspectra of these tori are calculated. Geometrical effects, such aslensing-induced self-occulation and multiple-image contribution are far moresignificant in accretion tori than geometrically thin accretion disks.Optically thin accretion tori emission line profiles are distinguishable fromthe profiles of lines from optically thick accretion tori and optically thickgeometrically thin accretion disks. Line profiles of optically thin accretiontori have a weaker dependence on viewing inclination angle than those of theoptically thick accretion tori or accretion disks, especially at high viewinginclination angles. Limb effects are present in accretion tori with finiteoptical depths. Finally, in accretion flows onto relativistic compact objects,gravitationally induced line resonance can occur. This resonance occurs easilyin 3D flows, but not in 2D flows, such as a thin accretion disk around a blackhole.

General relativistic radiative transfer: formulation and emission from structured tori around black holes