Coincident $$f(\mathbb {Q})$$ gravity: black holes, regular black holes, and black bounces

Abstract In this paper, we will use the coincident gauge to investigate new solutions of $$f(\mathbb {Q})$$ f ( Q ) theory applied in context black holes, regular and black-bounce spacetime. For each these approaches, compute linear with constraint that non-metricity scalar is zero. We also analyze geodesics solution interpret whether spacetime extensible or not, find Kretschmann determine regularity along spacetime, holes black-bounce, calculate energy conditions. latter case realize null condition ( NEC ), specifically $$NEC_1=WEC_1=SEC_1\leftrightarrow \rho +p_{r}\ge 0$$ N E C 1 = W S ↔ ρ + p r ≥ 0 , satisfied outside event horizon.