Polytropic Stars in $f(Q) = Q +\xi Q^2$ covariant formulation

TL;DR

This paper explores polytropic stars within a modified gravity framework based on symmetric teleparallelism, deriving new equations and analyzing their physical properties through numerical methods.

Contribution

It introduces a family of $f(Q)$ gravity models, derives their TOV equations for polytropic stars, and investigates their mass-radius relations and non-metricity behavior.

Findings

Derived TOV equations for $f(Q)$ gravity models.

Numerical solutions reveal maximum mass and radius relations.

Analyzed non-metricity behavior inside and outside stars.

Abstract

General Relativity (GR) is not the only way gravity can be geometrised. Instead of curvature, the Teleparallel Theory attributes gravity to torsion $T$, which is related to the antysimmetric part of connection, and the Symmetric Teleparallel theory no longer preserves metricity, describing gravity through the non-metricity tensor $Q_{\alpha\mu\nu}\equiv \nabla_\alpha g_{\mu\nu}.$ 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. Using numerical integration, it is possible to solve a system of differential equations and 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.