Bounds on M/R for Charged Objects with positive Cosmological constant

Håkan Andréasson; Christian G. Boehmer; Atifah Mussa

doi:10.1088/0264-9381/29/9/095012

paper

Bounds on M/R for Charged Objects with positive Cosmological constant

arXiv:1201.5725 · doi:10.1088/0264-9381/29/9/095012

Abstract

We consider charged spherically symmetric static solutions of the Einstein-Maxwell equations with a positive cosmological constant $Λ$ . If $r$ denotes the area radius, $m_{g}$ and $q$ the gravitational mass and charge of a sphere with area radius $r$ respectively, we find that for any solution which satisfies the condition $p + 2 p_{⊥} \leq ρ,$ where $p \geq 0$ and $p_{⊥}$ are the radial and tangential pressures respectively, $ρ \geq 0$ is the energy density, and for which $0 \leq \frac{q ^{2}}{r ^{2}} + Λ r^{2} \leq 1,$ the inequality $\frac{m _{g}}{r} \leq 2/9 + \frac{q ^{2}}{3 r ^{2}} - \frac{Λ r ^{2}}{3} + 2/9 1 + \frac{3 q ^{2}}{r ^{2}} + 3Λ r^{2}$ holds. We also investigate the issue of sharpness, and we show that the inequality is sharp in a few cases but generally this question is open.

12 pages. Revised version to appear in Class. Quant. Grav

Bounds on M/R for Charged Objects with positive Cosmological constant

Abstract

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