Illustration of the different reference frames: the black-hole frame (in black) (xbh,ybh,zbh) labeled in Kerr-Schild coordinates, where the zbh-axis corresponds to the angular momentum-axis; the orbit frame (in blue) (xorb,yorb,zorb); and finally, the observer frame (in green) (α,δ,zobs). The angles i′ and Ω′ allow to recover the direction of the angular momentum of the black hole; they give the position of the black-hole frame relative to the observer frame. The point P on the orbit of the star denotes the pericenter.
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