Håkan Andréasson, Christian Böhmer, Atifah Mussa
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 $\frac{m_g}{r} \leq 2/9+\frac{q^2}{r^2}-\frac{\Lambda
r^2}{3}+2/9\sqrt{1+\frac{3q^2}{r^2}+3\Lambda r^2}$ 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.
View original:
http://arxiv.org/abs/1201.5725
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