Spherically symmetric configuration in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>Q</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> 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--Nordstr\"om--de Sitter solution with an electromagnetic field. For internal structure, with a simple model $f(Q)=Q+\ensuremath{\alpha}{Q}^{2}$ and a polytropic equation of state, we find that a negative modification ($\ensuremath{\alpha}&lt;0$) provides support to more stellar masses while a positive one ($\ensuremath{\alpha}&gt;0$) reduces the amount of matter of the star.

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