Killing energy with positive time signature ($E=g(P,K)$)

With metric signature $(+---)$ and a future timelike stationary Killing vector $K$, positive energy is $E=g(P,K)$ for future physical momentum $P$. A common $(-+++)$ convention instead uses $-g(P,K)$. The normalization of $K$ fixes the observer or asymptotic time scale.