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This work outlines a straightforward mechanism for endorsing primary hairinto Schwarzschild black holes, resulting in a unique modification within theframework of a special scalar-tensor theory, the so-called beyond Horndeskitype. The derived solutions are exact, showcase primary hair with an everywhereregular scalar field profile, and continuously connect with the vacuumgeometry. Initially devised to introduce primary hair in spherically symmetricsolutions within General Relativity in any dimension, our investigation alsoexplores the conditions under which spherically symmetric black holes inalternative gravitational theories become amenable to the endorsement ofprimary hair through a similar pattern. As a preliminary exploration, we embarkon the process of endorsing primary hair to the Reissner-Nordstr\"om blackhole. Subsequently, we extend our analysis to encompass spherically symmetricsolutions within Lovelock and cubic quasitopological gravity theories.

Endorsing black holes with beyond Horndeski primary hair: An exact solution framework for scalarizing in every dimension