# UCL Discovery

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

Andréasson, H; Boehmer, CG; Mussa, A; (2012) Bounds on M/R for Charged Objects with positive Cosmological constant. Classical and Quantum Gravity , 29 095012 - ?. 10.1088/0264-9381/29/9/095012.

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## Abstract

We consider charged spherically symmetric static solutions of the Einstein-Maxwell equations with a positive cosmological constant $\Lambda$. 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 $p+2p_{\perp}\leq \rho,$ where $p\geq 0$ and $p_{\perp}$ are the radial and tangential pressures respectively, $\rho\geq 0$ is the energy density, and for which $0\leq \frac{q^2}{r^2}+\Lambda r^2\leq 1,$ the inequality $\frac{m_g}{r} \leq 2/9+\frac{q^2}{3r^2}-\frac{\Lambda r^2}{3}+2/9\sqrt{1+\frac{3q^2}{r^2}+3\Lambda r^2}$ 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.

Type: Article Bounds on M/R for Charged Objects with positive Cosmological constant 10.1088/0264-9381/29/9/095012 http://dx.doi.org/10.1088/0264-9381/29/9/095012 12 pages. Revised version to appear in Class. Quant. Grav gr-qc, gr-qc UCL > School of BEAMS > Faculty of Maths and Physical Sciences > MathematicsUCL > School of BEAMS > Faculty of Maths and Physical Sciences > Space and Climate Physics

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