Same exact Kerr metric as the 3D version, drawn two different, genuinely 2D ways instead of rendered as a 3D surface:
Top panel — meridional cross-section. Because the Kerr solution is axisymmetric, one vertical slice through the spin axis (the r–θ plane) fully determines the 3D shape by revolution. The horizon is a coordinate sphere r = r₊, so it slices to a circle. The ergosphere does not:
r₊ = 1 + √(1 − a²) event horizon (circle)
r_ergo(θ) = 1 + √(1 − a²cos²θ) ergosphere boundary (oblate curve)
At the poles (θ=0,π) the two curves touch; at the equator (θ=π/2) the ergosphere bulges out to a fixed 2M regardless of spin, while the horizon shrinks as a grows. The lens-shaped gap between the two curves near the equator is the ergosphere — the leftover fits both the pole-touching and higher spin= smaller horizon.
Bottom panel — angular-velocity graph. Instead of animating particles through 3D space, their exact orbital rate is plotted directly against radius, using the Bardeen–Press–Teukolsky formula for circular equatorial orbits:
Ω_orbit(r) = ±1 / (r^1.5 ± a) (+ prograde, − retrograde)
Ω_ZAMO(r) = 2a / (r³ + a²r + 2a²) frame-dragging rate of a "static" observer
The dashed grey Ω_ZAMO(r) curve is the Lense–Thirring dragging rate itself: even an observer trying to sit still at fixed angular position is forced to co-rotate at this rate once inside the ergosphere. Dropped test particles appear as small spinning dial glyphs sitting on their curve at their launch radius — the dial's hand angle is the particle's exact orbital phase φ(t), so its visible spin rate on screen is Ω(r,a) itself, no artistic license.
- Spin slider — reshapes both panels live: the ergosphere curve separates from the horizon circle, and the ISCO/photon-sphere marker lines slide along the graph.
- + Prograde / + Retrograde — drops a dial at the chosen launch radius on the corresponding curve.