Conical singularities and the Vainshtein screening in full GLPV theories
  In Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, it is known that the
conical singularity arises at the center of a spherically symmetric body
($r=0$) in the case where the parameter $\alpha_{{\rm H}4}$ characterizing the
deviation from the Horndeski Lagrangian $L_4$ approaches a non-zero constant as
$r \to 0$. We derive spherically symmetric solutions around the center in full
GLPV theories and show that the GLPV Lagrangian $L_5$ does not modify the
divergent property of the Ricci scalar $R$ induced by the non-zero
$\alpha_{{\rm H}4}$. Provided that $\alpha_{{\rm H}4}=0$, curvature scalar
quantities can remain finite at $r=0$ even in the presence of $L_5$ beyond the
Horndeski domain. For the theories in which the scalar field $\phi$ is directly
coupled to $R$, we also obtain spherically symmetric solutions inside/outside
the body to study whether the fifth force mediated by $\phi$ can be screened by
non-linear field self-interactions. We find that there is one specific model of
GLPV theories in which the effect of $L_5$ vanishes in the equations of motion.
We also show that, depending on the sign of a $L_5$-dependent term in the field
equation, the model can be compatible with solar-system constraints under the
Vainshtein mechanism or it is plagued by the problem of a divergence of the
field derivative in high-density regions.
