Spherically symmetric configuration in f ( Q ) gravity

General relativity can be formulated equivalently with a non-Riemannian geometry that associates with an affine connection of nonzero nonmetricity Q but vanishing curvature R and torsion T. Modification based on this description of gravity generates the f(Q) gravity. In this work, we explore the application of f(Q) gravity to the spherically symmetric configurations. We discuss the gauge fixing and connections in this setting. We demonstrate the effects of f(Q) by considering the external and internal solutions of compact stars. The external background solutions for any regular form of f(Q) coincide with the corresponding solutions in general relativity, i.e., the Schwarzschild–de Sitter solution and the Reissner–Nordström–de Sitter solution with an electromagnetic field. For internal structure, with a simple model f(Q)=Q+αQ2 and a polytropic equation of state, we find that a negative modification (α0) reduces the amount of matter of the star.