Neutron stars in $f(\mathbb{Q})$ gravity

TL;DR

This paper explores the construction of neutron star solutions in $f( ext{Q})$ gravity, emphasizing the role of the affine connection and the conditions under which solutions deviate from General Relativity, providing a framework for future numerical studies.

Contribution

It clarifies the conditions leading to GR-like behavior in $f( ext{Q})$ gravity neutron stars and develops a boundary value problem approach to study beyond-GR solutions.

Findings

Solutions tend to recover GR dynamics under standard assumptions.

The connection's dynamics constrain the asymptotic behavior of solutions.

Formulation of a boundary value problem highlights numerical challenges.

Abstract

We investigate the challenges of constructing neutron star (NS) solutions in $f(\mathbb{Q})$ gravity, highlighting the importance of treating the affine connection as an active, dynamical component of the theory. We begin by clarifying under what conditions standard simplifications -- such as the coincident gauge or General Relativity (GR)-like connections -- inadvertently lead to GR behavior, even in non-trivial $f(\mathbb{Q})$ models. Building on previous work in black hole (BH) spacetimes, we adapt the formalism to NS and extend it to non-vacuum configurations. Focusing on two representative models, $f(\mathbb{Q}) = \mathbb{Q} + \alpha \mathbb{Q}^2$ and $f(\mathbb{Q}) = \mathbb{Q}^\beta$, our analysis suggests that, under standard regularity assumptions, solutions with Maclaurin/Laurent-type series recover GR dynamics, pointing to more intricate structures as the likely seat of beyond-GR effects, and reflecting the constraints imposed by the connection's dynamics on the asymptotic behavior of genuinely beyond-GR solutions. We then formulate the problem as a boundary value problem (BVP) and highlight the numerical pathologies that may arise, together with possible strategies to prevent them. This work aims to provide a concrete framework for future numerical studies and outlines the theoretical consistency conditions required to construct physically meaningful beyond-GR NS solutions in $f(\mathbb{Q})$ gravity.