 Kerr ergoregion

The Kerr ergoregion is the region where the asymptotically timelike stationary Killing field becomes spacelike. Its outer boundary is $r=M+\sqrt{M^2-a^2{\cos }^2\theta }$.

The Kerr realization of an ergosphere lies outside the outer horizon where the stationary Killing vector is spacelike; its outer boundary is $r=M+\sqrt{M^2-a^2{\cos }^2\theta }$.