Uploaded March 2011 | Updated September 2026, 2 weeks ago
*** Please view the video youtube.com/watch?v=T_TU6T4-0LU (which explores the exact same black hole, but in a different trajectory) before this one, as it provides more explanation of what is going on! ***
Journey of an observer perpetually stuck between the horizons of a(n ideal) Kerr black hole. (Here, the black hole has a mass of roughly one million solar masses (Schwarzschild radius = 10 light seconds) and an angular momentum at 80% of maximality (a/M=0.8).) Such a remarkable trajectory (or "lazy geodesic") has no energy and no angular momentum, and this one moreover remains in the equatorial plane; in Boyer-Lindquist coordinates, it seems to bounce back and forth between the outer and inner horizons (on this video, it starts halfway between them and going down), but it does so at "constant time". In the Penrose diagram, it is moving across universes, from black hole ("going down") to white hole ("going up") regions II again and again, never emerging to regions I and never entering regions III); the period of the motion, in the observer's proper time, is π times the Schwarzschild radius of the black hole.
In the video, a blue sphere is placed outside the black hole at some distance (in every region I, but with a slightly different color of blue to differentiate sibling regions I), and the outer and inner horizons are various shades of red and green (red/orange/brown for outer, green for inner; lighter shades are white hole horizons, darker shades are black hole horizons). All spheres are checkered in an identical way, with twenty-four longitudinal stripes and twelve latitudinal (or polar) stripes, consistent with the black hole's axis. (The longitudinal stripes on the horizons rotate with the black hole.)
More explanation, other videos and higher quality download ← madore.org/~david/math/kerr.html
*** Please view the video youtube.com/watch?v=T_TU6T4-0LU (which explores the exact same black hole, but in a different trajectory) before this one, as it provides more explanation of what is going on! ***
Journey of an observer perpetually stuck between the horizons of a(n ideal) Kerr black hole. (Here, the black hole has a mass of roughly one million solar masses (Schwarzschild radius = 10 light seconds) and an angular momentum at 80% of maximality (a/M=0.8).) Such a remarkable trajectory (or "lazy geodesic") has no energy and no angular momentum, and this one moreover remains in the equatorial plane; in Boyer-Lindquist coordinates, it seems to bounce back and forth between the outer and inner horizons (on this video, it starts halfway between them and going down), but it does so at "constant time". In the Penrose diagram, it is moving across universes, from black hole ("going down") to white hole ("going up") regions II again and again, never emerging to regions I and never entering regions III); the period of the motion, in the observer's proper time, is π times the Schwarzschild radius of the black hole.
In the video, a blue sphere is placed outside the black hole at some distance (in every region I, but with a slightly different color of blue to differentiate sibling regions I), and the outer and inner horizons are various shades of red and green (red/orange/brown for outer, green for inner; lighter shades are white hole horizons, darker shades are black hole horizons). All spheres are checkered in an identical way, with twenty-four longitudinal stripes and twelve latitudinal (or polar) stripes, consistent with the black hole's axis. (The longitudinal stripes on the horizons rotate with the black hole.)
More explanation, other videos and higher quality download ← madore.org/~david/math/kerr.html
