Polytropic stars in f(Q)=Q+ξQ2 covariant formulation

General Relativity (GR) is not the only way gravity can be geometrized. Instead of curvature, the Teleparallel Theory attributes gravity to the torsion T , which is related to the antisymmetric part of the connection. On the other hand, the Symmetric Teleparallel Theory no longer preserves metricity, describing gravity through the non-metricity tensor Qαμν ≡ ∇ α gμν . These descriptions give form to what is known as geometrical trinity of gravity. Recently, the extensions of GR have been intensively investigated in order to solve the theoretical impasses which have arisen. In this sense, it is also useful to investigate the extensions of alternative descriptions of gravity, which leads us to the so-called f ( T ) and f ( Q ) gravities. In this paper, we consider a family of f ( Q ) models and obtain their corresponding Tolman-Oppenheimer-Volkoff equations applied to polytropic stars. It is worth mentioning that the f ( Q ) covariant formulation is adopted and we present a new equation that substantially simplifies the numerical calculations. Using numerical integration, it is possible to solve a system of differential equations to calculate, among other things, the maximum mass and mass-radius relation allowed. In addition, we explicitly show the non-metricity behavior inside and outside the star.