Static plane symmetric solutions in f(Q) gravity

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+α 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 α with larger magnitude leads to higher internal pressure and a thicker slab, while models with positive α α are incompatible with a self-gravitating slab of positive pressure.