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In this work, we delve into the model of the shift symmetric andparity-preserving Beyond Horndeski theory in all its generality. We present anexplicit algorithm to extract static and spherically symmetric black holes withprimary scalar charge adhering to the conservation of the Noether currentemanating from the shift symmetry. We show that when the functionals $G_2$ and$G_4$ of the theory are linearly dependent, analytic homogeneous black-holesolutions exist, which can become regular by virtue of the primary chargecontribution. Such geometries can easily enjoy the preservation of the WeakEnergy Conditions, elevating them into healthier compact objects than mosthairy black holes in modified theories of gravity. Finally, we revisit theconcept of disformal transformations as a solution-generating mechanism anddiscuss the case of generic $G_2$ and $G_4$ functionals.

Compact objects with primary hair in shift and parity symmetric beyond Horndeski gravities