Existence and disappearance of conical singularities in Gleyzes-Langlois-Piazza-Vernizzi theories

Understand

In a class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, we derive both vacuum and interior Schwarzschild solutions under the condition that the derivatives of a scalar field $\phi$ with respect to the radius $r$ vanish.

• If the parameter $\alpha_{\rm H}$ characterizing the deviation from Horndeski theories approaches a non-zero constant at the center of a spherically symmetric body, we find that the conical singularity arises at $r=0$ with the Ricci scalar given by $R=-2\alpha_{\rm H}/r^2$.
• This originates from violation of the geometrical structure of four-dimensional curvature quantities.
• The conical singularity can disappear for the models in which the parameter $\alpha_{\rm H}$ vanishes in the limit that $r \to 0$.