Coincident

In this paper, we will use the coincident gauge to investigate new solutions of the $$f(\mathbb {Q})$$ theory applied in the context of black holes, regular black holes, and the black-bounce spacetime. For each of these approaches, we compute the linear solutions and the solutions with the constraint that the non-metricity scalar is zero. We also analyze the geodesics of each solution to interpret whether the spacetime is extensible or not, find the Kretschmann scalar to determine the regularity along spacetime, and in the context of regular black holes and black-bounce, we calculate the energy conditions. In the latter black-bounce case we realize that the null energy condition (NEC), specifically the $$NEC_1=WEC_1=SEC_1\leftrightarrow \rho +p_{r}\ge 0$$, is satisfied outside the event horizon