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.
Categories: gr-qc