  Recent observations show strong evidence for the presence of Doppler-shifted
emission lines in the spectrum of both black hole candidates and active
galactic nuclei. These lines are likely to originate from relativistic outflows
(or jets) in the vicinity of the central black hole. Consequently, the profile
of such a line should be distorted by strong gravitational effects near the
black hole, as well as special relativistic effects. In this paper, we present
results from a detailed study on how each process affects the observed line
profile. We found that the profile is sensitive to the intrinsic properties of
the jets (Lorentz factor, velocity profile, and emissivity law), as well as to
the spin of the black hole and the viewing angle (with respect to the axis of
the jets). More specifically, in the case of approaching jets, an intrisically
narrow line (blue-shifted) is seen as simply broadened at small viewing angles,
but it shows a doubly peaked profile at large viewing angles for extreme Kerr
black holes (due to the combination of gravitational focusing and Doppler
effects); the profile is always singly peaked for Schwarzschild black holes.
For receding jets, however, the line profile becomes quite complicated owing to
complicated photon trajectories. To facilitate comparison with observations, we
searched a large parameter space to derive representative line profiles. We
show the results and discuss how to use emission lines as a potential tool for
probing the inner region of a black hole jet system.
