Ergoregion of a stationary spacetime ($g(k,k)>0$)

For a chosen stationary time-translation Killing vector field $k$, this is the region where $k$ is spacelike and observers following its orbits cannot be timelike. In an asymptotically flat geometry, the usual choice is the nonrotating time translation at infinity. The stationary-limit boundary has $g(k,k)=0$, but need not be an event horizon. The Kerr ergoregion is a particular rotating-black-hole example: its outer boundary touches the horizon only on the axis for nonzero subextremal spin.