Inequalities relating area, energy, surface gravity and charge of black holes

Details Inequalities relating area, energy, surface gravity and charge of black holes Inequalities relating area, energy, surface gravity and charge of black holes

1998-07-02

arxiv.org/abs/gr-qc/9807003v1

Phys.Rev.Lett.81:4557-4559,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

3 pages, revtex

Scientific paper

10.1103/PhysRevLett.81.4557

The Penrose-Gibbons inequality for charged black holes is proved in spherical symmetry, assuming that outside the black hole there are no current sources, meaning that the charge e is constant, with the remaining fields satisfying the dominant energy condition. Specifically, for any achronal hypersurface which is asymptotically flat at spatial or null infinity and has an outermost marginal surface 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 black hole. A recent definition of dynamic surface gravity k also satisfies inequalities 2k <= 1/r - e^2/r^3 and m >= r^2 k + e^2/r. All these inequalities are sharp in the sense that equality is attained for the Reissner-Nordstrom black hole.

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