Spherically symmetric configuration in $f(Q)$ gravity

TL;DR

This paper investigates spherically symmetric solutions in $f(Q)$ gravity, showing that external solutions match general relativity, while internal stellar structures are affected by the form of $f(Q)$, influencing star mass and matter content.

Contribution

It provides the first detailed analysis of spherically symmetric configurations in $f(Q)$ gravity, including external and internal solutions with specific effects on stellar properties.

Findings

External solutions match GR solutions like Schwarzschild-de Sitter.

Negative $\alpha$ in $f(Q)$ supports more massive stars.

Positive $\alpha$ reduces stellar matter content.

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-Nordstr\"om-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.