Instability of Static Semi-Closed Worlds in Generalized Galileon Theories

We consider generalized Galileon theories within general relativity in four-dimensional space-time. We provide the argument showing that the generalized Galileons described by a wide class of Lagrangians do not admit stable, static, spherically symmetric semi-closed worlds. We also show that in a class of theories with $p_{\perp} = - \rho$ (where $p_{\perp}$ is transverse pressure and $\rho$ is energy density), semi-closed worlds, if exist, would be observed as objects of negative mass.