We analytically compute the observational appearance of an isotropically
emitting point source on a circular, equatorial orbit near the horizon of a
rapidly spinning black hole. The primary image moves on a vertical line
segment, in contrast to the primarily horizontal motion of the spinless case.
Secondary images, also on the vertical line, display a rich caustic structure.
If detected, this unique signature could serve as a "smoking gun" for a
high-spin black hole in nature.Comment: 36 pages, 6 figures. v2: added a figure and improved section 4.1,
matches published version. Related videos available at
https://youtu.be/ZRfTj5JKPkA and https://youtu.be/K0jEa0Q9NJ
