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While the test particle falls into the rotating black hole in a finite proper time, it makes an infinite amount of revolutions while frozen on the horizon from the perspective of a coordinate observer. Units of time are in GM/c³. The spin parameter is 0.9, the initial distance 3GM/c² and the polar launch angle 36°. The initial velocity in a prograde direction is the newtonian orbital velocity. The length of the red tail is 1/4 GM/c³ in proper time (at the horizon it becomes infinitely long after an infinite amount of coordinate time and in a finite proper time because of gravitational time dilation and the frame-dragging-effect).
Summary
DescriptionGravitational time dilation around a black hole.gif
The proper time of a particle spiraling into a rotating black hole (left) and the coordinate time in which an observer at infinity observes the particle (right)
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