Spherically symmetric configuration in $f(Q)$ gravity

Abstract

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 $f(Q)=Q+\alpha Q^2$ and a polytropic equation of state, we find that a negative modification ($\alpha <0$) provides support to more stellar masses while a positive one ($\alpha >0$) reduces the amount of matter of the star.

21 pages, 3 figures, typos corrected, matching the published version

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• Coincident f(Q) gravity: black holes, regular black holes and black bounces
• Coincident gauge for static spherical field configurations in symmetric teleparallel gravity
• Buchdahl quark stars within $f(Q)$ theory
• Comment on "Energy conditions in $f(Q)$ gravity"
• Coupling matter and curvature in Weyl geometry: conformally invariant $f\left(R,L_m\right)$ gravity
• Constraining study of charged gravastars solutions in symmetric teleparallel gravity
• Non-exotic static spherically symmetric thin-shell wormhole solution in $f(Q,T)$ gravity
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