  We study and quantify gravitational redshift by means of relativistic ray
tracing simulations of emission lines. The emitter model is based on thin,
Keplerian rotating rings in the equatorial plane of a rotating black hole.
Emission lines are characterised by a generalized fully relativistic Doppler
factor or redshift associated with the line core. Two modes of gravitational
redshift, shift and distortion, become stronger with the emitting region closer
to the Kerr black hole. Shifts of the line cores reveal an effect at levels of
0.0015 to 60 % at gravitational radii ranging from 100000 to 2. The
corresponding Doppler factors range from 0.999985 to 0.4048. Line shape
distortion by strong gravity, i.e. very skewed and asymmetric lines occur at
radii smaller than roughly ten gravitational radii. Gravitational redshift
decreases with distance to the black hole but remains finite due to the
asymptotical flatness of black hole space-time. The onset of gravitational
redshift can be tested observationally with sufficient spectral resolution.
Assuming a resolving power of ~100000, yielding a resolution of ~0.1 Angstroms
for optical and near-infrared broad emission lines, the gravitational redshift
can be probed out to approximately 75000 gravitational radii. In general,
gravitational redshift is an indicator of black hole mass and spin as well as
for the inclination angle of the emitter, e.g. an accretion disk. We suggest to
do multi-wavelength observations because all redshifted features should point
towards the same central mass.
