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The Penrose-Gibbons inequality for charged black holes is proved in sphericalsymmetry, assuming that outside the black hole there are no current sources,meaning that the charge e is constant, with the remaining fields satisfying thedominant energy condition. Specifically, for any achronal hypersurface which isasymptotically flat at spatial or null infinity and has an outermost marginalsurface of areal radius r, the asymptotic mass m satisfies 2m >= r + e^2/r.Replacing m by a local energy, the inequality holds locally outside the blackhole. A recent definition of dynamic surface gravity k also satisfiesinequalities 2k <= 1/r - e^2/r^3 and m >= r^2 k + e^2/r. All these inequalitiesare sharp in the sense that equality is attained for the Reissner-Nordstromblack hole.Comment: 3 pages, revte

Inequalities Relating Area, Energy, Surface Gravity, and Charge of Black Holes