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We describe the self-adjoint realizations of the operator $H:=-i\alpha\cdot\nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)=|x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda\alpha\cdot{x}/{|x|}\,\beta)$, for $\nu,\mu,\lambda \in \mathbb R$. Wecharacterize the self-adjointness in terms of the behaviour of the functions ofthe domain in the origin, exploiting Hardy-type estimates and trace lemmas.Finally, we describe the distinguished extension.

Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials