Abstract We systematically investigate static plane symmetric configurations in f (Q) gravity. For vacuum regions, we discuss the constancy of the nonmetricity scalar Q and derive general vacuum solutions, which correspond effectively to Taub- (anti) de Sitter spacetimes with a cosmological constant determined by the specific f (Q) model. By matching a singular thin shell source to the vacuum solutions, we relate the shell’s energy density and pressure to the integration constants of the exterior geometry. We also examine a finite-thickness slab as another matter source supporting the vacuum solution. Through numerical analysis of a quadratic model f (Q) =Q+ Q² f (Q) = Q + α Q 2 with isotropic matter, we show that the maximum pressure inside the slab generally does not coincide with the geometric center. Moreover, a negative α with larger magnitude leads to higher internal pressure and a thicker slab, while models with positive α are incompatible with a self-gravitating slab of positive pressure.
Long et al. (Tue,) studied this question.