General Relativity: An Introduction for Physicists · Problem 13.8
The Kerr geometry — Hobson, Efstathiou & Lasenby
Physics · kerr-ergoregion-angular-velocity
Problem
An observer is at fixed (r,θ) coordinates in the ergoregion of a Kerr black hole and has angular velocity Ω=dϕ/dt with respect to a second observer at rest at infinity. Show that the allowed range for Ω is given by Ω−<Ω<Ω+, where
Ω±=ω±c(Σ2Δ)1/2
and ω, Δ and Σ2 have their usual meanings in the Kerr metric.