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 α_H4 characterizing the deviation from the Horndeski Lagrangian L₄ approaches a non-zero constant as r 0. We derive spherically symmetric solutions around the center in full GLPV theories and show that the GLPV Lagrangian L₅ does not modify the divergent property of the Ricci scalar R induced by the non-zero α_H4. Provided that α_H4 = 0, curvature scalar quantities can remain finite at r = 0 even in the presence of L₅ beyond the Horndeski domain. For the theories in which the scalar field φ is directly coupled to R, we also obtain spherically symmetric solutions inside/outside the body to study whether the fifth force mediated by φ 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 L₅ vanishes in the equations of motion. We also show that, depending on the sign of a L₅-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.