Bounds on M/R for static objects with a positive cosmological constant

We consider spherically symmetric static solutions of the Einstein equations with a positive cosmological constant Lambda, which are regular at the centre, and we investigate the influence of Lambda on the bound of M/R, where M is the ADM mass and R is the area radius of the boundary of the static object. We find that for any solution which satisfies the energy condition p + 2p(perpendicular to) <= rho, where p >= 0 and p(perpendicular to) are the radial and tangential pressures respectively, and rho >= 0 is the energy density, and for which 0 <= Lambda R-2 <= 1, the inequality