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In Gleyzes-Langlois-Piazza-Vernizzi (GLPV) scalar-tensor theories, which areoutside the domain of second-order Horndeski theories, it is known that thereexists a solid angle deficit singularity in the case where the parameter$\alpha_{\rm H}$ characterizing the deviation from Horndeski theoriesapproaches a non-vanishing constant at the center of a spherically symmetricbody. Meanwhile, it was recently shown that second-order generalized Procatheories with a massive vector field $A^{\mu}$ can be consistently extended tobeyond-generalized Proca theories, which recover shift-symmetric GLPV theoriesin the scalar limit $A^{\mu} \to \nabla^{\mu} \chi$. In beyond-generalizedProca theories up to quartic-order Lagrangians, we show that solid angledeficit singularities are generally absent due to the existence of a temporalvector component. We also derive the vector-field profiles around a compactobject and show that the success of the Vainshtein mechanism operated by vectorGalileons is not prevented by new interactions in beyond generalized Procatheories.

Absence of solid angle deficit singularities in beyond-generalized Proca theories