General Relativity: An Introduction for Physicists · Problem 13.17
The Kerr geometry — Hobson, Efstathiou & Lasenby
Physics · kerr-ergoregion-orbit-constraints
Problem
Suppose that the circular orbit considered in Exercise 13.16 lies outside the horizon r+ but inside the stationary limit rS+. Show that under these circumstances Ω must be non-zero, i.e. the observer cannot remain at rest relative to a distant observer. If the orbiting observer is in the region r−<r<r+, show that the orbit cannot be circular.