Instability of static semiclosed worlds in generalized Galileon theories

We consider generalized Galileon theories within general relativity in four-dimensional spacetime. We provide the argument showing that the generalized Galileons described by a wide class of Lagrangians do not admit stable, static, spherically symmetric semiclosed 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), semiclosed worlds, if they exist, would be observed as objects of negative mass.

Figure 1

Semiclosed world.

Figure 2

Behavior of $c(r)$ for a semiclosed world.