In recent years, Poincaré gauge gravity theory has attracted widespread attention and application in 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, Given the significance of Poincaré gauge gravity theory, it is essential to investigate the properties of neutron stars within the framework of this theory, and to examine whether observations of neutron stars can be used to distinguish and test Poincaré gauge gravity theory versus general relativity.
In this paper, we select a specific gravitational field Lagrangian for Poincaré gauge gravity theory to derive the corresponding gravitational field equations. Based on these equations, we further derive the modified Tolman-Oppenheimer-Volkoff (TOV) equation for spherically symmetric static neutron stars. When the spacetime torsion is zero, the modified static neutron star TOV equation reduces precisely to the TOV equation in general relativity.
We then proceed to investigate the impact of torsion on the mass-radius relation of static neutron stars. Our analysis shows that, in a 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 results 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, we discuss the effects of neutron star rotation and find that the selected Poincaré gauge gravity model is not suitable for investigating the mass–radius relation of rotating neutron stars. This work provides a theoretical foundation and reference methods for further research on the mass–radius relation of rotating neutron stars within the framework of Poincaré gauge gravity.