= Reissner-Nordstrom horizon surface gravity
{c}
{title2=$\kappa_+=(r_+-r_-)/(2r_+^2)$}
For $M>0$ and $M\geq|Q|$, put $r_\pm=M\pm\sqrt{M^2-Q^2}$. The stationary <Killing vector field> normalized at infinity generates the outer <Killing horizon>. In an ingoing null chart its covector is $dr$ on that horizon; the <Killing equation> then gives $\nabla_k k=\tfrac12 f'(r_+)k$, where $f=(r-r_+)(r-r_-)/r^2$. Thus the positive nonextremal <surface gravity> is $(r_+-r_-)/(2r_+^2)$. It tends to zero when $M=|Q|$, where the horizon becomes a <degenerate Killing horizon>. The past horizon branch has the opposite signed nonaffinity for the same time-translation field.
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