  Observational efforts to image the immediate environment of a black hole at
the scale of the event horizon benefit from the development of efficient
imaging codes that are capable of producing synthetic data, which may be
compared with observational data. We aim to present RAPTOR, a new public code
that produces accurate images, animations, and spectra of relativistic plasmas
in strong gravity by numerically integrating the equations of motion of light
rays and performing time-dependent radiative transfer calculations along the
rays. The code is compatible with any analytical or numerical spacetime. It is
hardware-agnostic and may be compiled and run both on GPUs and CPUs. We
describe the algorithms used in RAPTOR and test the code's performance. We have
performed a detailed comparison of RAPTOR output with that of other
radiative-transfer codes and demonstrate convergence of the results. We then
applied RAPTOR to study accretion models of supermassive black holes,
performing time-dependent radiative transfer through general relativistic
magneto-hydrodynamical (GRMHD) simulations and investigating the expected
observational differences between the so-called fast-light and slow-light
paradigms. Using RAPTOR to produce synthetic images and light curves of a GRMHD
model of an accreting black hole, we find that the relative difference between
fast-light and slow-light light curves is less than 5%. Using two distinct
radiative-transfer codes to process the same data, we find integrated flux
densities with a relative difference less than 0.01%. For two-dimensional GRMHD
models, such as those examined in this paper, the fast-light approximation
suffices as long as errors of a few percent are acceptable. The convergence of
the results of two different codes demonstrates that they are, at a minimum,
consistent.
