In the opening paragraph of section 6.3 Carroll defines a killing horizon to be a null hypersurface Σ where some killing vector field χμ becomes null. Later (on page 247 if you have the book) when distinguishing between static and stationary space times, he says that in a stationary, but not static spacetime, we still have the killing field Kμ = (∂t)μ , but it wont become null at the killing horizon. How is that possible? By definition that seems wrong. How do you have a killing horizon if thats not where your killing field becomes null?