Surface gravity from the Killing derivative
= Surface gravity from the Killing derivative
{title2=$\kappa^2=-\tfrac12(\nabla_aK_b)(\nabla^aK^b)$}
At a regular <Killing horizon>, the generator is hypersurface orthogonal and satisfies $\nabla_KK=\kappa K$. The <Killing derivative contraction identity> gives the displayed squared <surface gravity>, including through a <bifurcation surface> by continuity. The generator's normalization is part of this formula.