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

TL;DR

This work investigates whether neutron stars can exhibit genuinely beyond-GR behavior in $f(\mathbb{Q})$ gravity by treating the affine connection as a dynamical field. It develops a stationary, spherically symmetric framework with a perfect-fluid source and analyzes two representative models, $f(\mathbb{Q})=\mathbb{Q}+\alpha\mathbb{Q}^2$ and $f(\mathbb{Q})=\mathbb{Q}^{\beta}$, deriving the full set of metric and connection equations under minimal matter coupling. The authors show that, under regularity and standard boundary conditions, solutions admitting Maclaurin/Laurent expansions tend to GR, suggesting beyond-GR effects require non-analytic radial structures and careful treatment of the connection’s dynamics, especially for asymptotics. They discuss numerical pathologies that plague naive shooting methods and advocate global boundary-value problem approaches with continuation in deformation parameters to preserve the connection’s degrees of freedom. The paper provides a clear methodological roadmap and consistency criteria for future numerical explorations of beyond-GR NS solutions in $f(\mathbb{Q})$ gravity, clarifying when and how deviations from GR might arise and how to detect them in practice.

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, $f(\mathbb{Q}) = \mathbb{Q} + α\mathbb{Q}^2$ and $f(\mathbb{Q}) = \mathbb{Q}^β$, 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.