  The region of spacetime near the event horizon of a black hole can be viewed
as a deep potential well at large gravitational redshift relative to distant
observers. However, matter orbiting in this region travels at relativistic
speeds and can impart a significant Doppler shift to its electromagnetic
emission, sometimes resulting in a net observed blueshift at infinity. Thus, a
black hole broadens the line emission from monochromatic sources in its
vicinity into a smoothly decaying "red wing"--whose flux vanishes at large
redshift--together with a "blue blade" that retains finite flux up to a sharp
edge corresponding to the maximum observable blueshift. In this paper, we study
the blue blade produced by isotropic monochromatic emitters on circular
equatorial orbits around a Kerr black hole, and obtain simple relations
describing how the maximum blueshift encodes black hole spin and inclination.
We find that small values of the maximum blueshift yield an excellent probe of
inclination, while larger values provide strong constraints on spin or
inclination in terms of the other. These results bear direct relevance to
ongoing and future observations aiming to infer the angular momentum of
supermassive black holes from the broadening of their surrounding line
emission.
