While reading the paper "Disorder horizons: Holography of randomly disordered fixed points" by Hartnoll and Santos, I came across this:
We are interested in solutions with a zero temperature horizon. This not only means that there is one time-like Killing vector field $\partial_t$, but also that the norm of $\partial_t$ must vanish at least quadratically at the extremal horizon.
What is a zero temperature horizon and how is it related to the time-like Killing vector field?
