In recent years, Poincaré gauge gravity theory has attracted widespread attention and has been applied to the fields of gravitation and astrophysics. Therefore, how to distinguish between general relativity and Poincaré gauge gravity theory through experimental observations has become an important subject. The core of Poincaré gauge gravity theory is the introduction of torsion in spacetime. General relativity can be regarded as a special case of Poincaré gauge gravity theory in the absence of torsion. Neutron stars, as celestial bodies with extremely strong gravitational fields, serve as an ideal laboratory for Poincaré gauge gravity theory. At present, research on the properties of neutron stars based on the Poincaré gauge theory of gravitation is very scarce. In view of the significance of Poincaré gauge gravity theory, it is necessary to study the properties of neutron stars within the framework of this theory and check whether observations of neutron stars can be used to distinguish and test Poincaré gauge gravity theory and general relativity.

In this work, a specific gravitational field Lagrangian is chosen for Poincaré gauge gravity theory to derive the corresponding gravitational field equations. Based on these equations, the modified Tolman-Oppenheimer-Volkoff (TOV) equation is further derived for spherically symmetric static neutron stars. When the spacetime torsion is zero, the modified static neutron star TOV equation decreases precisely to the TOV equation in general relativity.

Then, the influence of torsion on the mass-radius relation of static neutron stars is investigated. Our analysis shows that in spherically symmetric spacetime, when the neutron star is static and only the spin tensor of particles is considered (the order of magnitude is 10^ - 34), the mass-radius relation of static neutron stars calculated by this theoretical model is consistent with the result in general relativity. This indicates that under static conditions, the correction effect of torsion on the mass-radius relation of neutron stars can be neglected.

This study is limited to static neutron star models under the condition of spherically symmetric spacetime metrics. However, in realistic astrophysical environments, neutron stars possess significant angular momentum. In the final section of this paper, the effect of neutron star rotation is discussed and the selected Poincaré gauge gravity model is found to be unsuitable for investigating the mass–radius relation of rotating neutron stars. This work provides a theoretical foundation and reference methods for further investigating the mass–radius relation of rotating neutron stars within the framework of Poincaré gauge gravity.