Testing linear non-minimal coupling in f(Q,T) gravity using X-ray binary pulsars constrained by NICER observations

Abstract

X-ray binary pulsars are valuable for testing alternative gravity theories like $f(Q,T)$ gravity because they host neutron stars (NSs) with strong gravitational fields and measurable matter interactions. The linear non-minimal coupling between $Q$ and $T$ can affect the star’s structure and emission, which Neutron Star Interior Composition Explorer (NICER) can constrain through high-precision X-ray timing and spectral data. In this work, we explore the physical implications of such couplings within the $f(Q,T)={\chi }_{1}Q+{\chi }_{2}T$ gravity framework, focusing on realistic, anisotropic stellar configurations. Using analytical methods, we model spherically symmetric NSs and calibrate our approach against well-observed pulsars including Her X-1, 4U 1538-52, and SMC X-1. The resulting configurations satisfy essential physical requirements: positive, finite energy density and pressure profiles; regularity at the center; vanishing radial pressure at the surface; and stable, causal behavior throughout. Pressure anisotropy remains positive, contributing to hydrostatic balance via a repulsive force that opposes gravity. The radial and tangential sound speeds remain subluminal, and the adiabatic index $\Gamma$ exceeds $4/3$ across the star, increasing outward—indicating resistance to collapse under perturbations. The $M-R$ relations predicted by the model align well with observations. For example, with ${\chi }_1=0.8$, we find $M\approx 0.95,M_{\odot }$ and $R\approx 9.18$ km; increasing ${\chi }_1$ to 1.0 gives $M\approx 1.19,M_{\odot }$ and $R\approx 11.39$ km. Similarly, for ${\chi }_2=0.0$, we obtain $M\approx 1.21,M_{\odot }$ and $R\approx 11.61$ km, while increasing ${\chi }_2$ to 0.8 yields $M\approx 1.19,M_{\odot }$ and $R\approx 11.38$ km. These trends highlight the role of ${\chi }_1$ and ${\chi }_2$ in controlling stellar compactness and stiffness. The model naturally captures a broad range of NS configurations, without relying on a fixed equation of state (EOS), and remains consistent with nuclear saturation density constraints. Altogether, these results establish $f(Q,T)$ gravity as a physically robust and observationally viable extension of general relativity (GR)—one capable of capturing the internal dynamics of compact stars with precision.