Kerr Black Hole
A spinning black hole drags spacetime around with it. Inside the ergosphere (outside the event horizon), no observer can stand still — even light is forced to corotate. This is frame dragging: rotation of mass causes rotation of spacetime itself. Roy Kerr solved the Einstein equations for this geometry in 1963 — sixty years after Schwarzschild's static solution.
singularity (ring)
event horizon r₊
ergosphere r_E
test particles (dragged)
ergosphere r_E/M (eq.)
2.000
why spinning mass drags spacetime
The Kerr metric in Boyer-Lindquist coordinates has an off-diagonal g_(tφ) term — pure relativistic frame dragging. Two key surfaces emerge for a black hole of mass M and angular momentum J (parameter a = J/M):
• Event horizon at r_± = M ± √(M² − a²) — the inner and outer horizons. Crossing r₊ is one-way.
• Ergosphere (static limit) at r_E(θ) = M + √(M² − a²cos²θ) — a flattened-pumpkin surface that bulges out at the equator, touching r₊ at the poles.
Between the ergosphere and the horizon, you cannot stay still: no timelike worldline holds constant (t, r, θ, φ). You must corotate with the hole. Light is dragged. Spacetime literally spins along.
Penrose process (Roger Penrose, 1969): drop an object into the ergosphere. Have it split — one piece gains negative energy and falls through r₊, the other escapes with more energy than the original. The extra energy comes from the hole's rotation. Up to 1 − 1/√2 ≈ 29.3% of a maximal Kerr's mass-energy is extractable.
Astrophysical Kerr: real black holes spin. Sgr A* is estimated at a/M ≈ 0.5–0.9. M87* has a/M ≈ 0.94. The Blandford-Znajek mechanism — magnetic field lines anchored in the ergosphere — powers relativistic jets in active galactic nuclei. The energy of gamma-ray bursts and quasars likely comes from Kerr rotation.
Inner mystery: the singularity inside a Kerr black hole is a ring, not a point. Passing through the ring (theoretically) sends you to a region of closed timelike curves — naked time travel. The Cauchy horizon at r₋ is mass-inflation unstable, so this is probably never reachable in nature. But the math is there.