Surface gravity of a five-dimensional charged black hole (${\kappa }_{\pm }=\pm 2\sqrt{M^2-Q^2}/r_{\pm }^3$)

The time translation is normalized at infinity. For the roots $r_{\pm }^2=M\pm \sqrt{M^2-Q^2}$, evaluate $V^{\prime }(r)/2$ to get the signed horizon values. The outer Hawking temperature in natural units is $\sqrt{M^2-Q^2}/(\pi r_{+}^3)$. The extremal limit has zero surface gravity; the neutral case has only the outer positive-radius horizon and temperature $1/(2\pi \sqrt{2M})$.