Neutron stars in Poincar\'e gauge gravity with quadratic torsion

Abstract

We study static neutron stars in an algebraic sector of Poincar\'e gauge gravity with parity-even and parity-odd quadratic torsion invariants. Since torsion is non-propagating, the contorsion equation is algebraic and can be solved in terms of the spin current. For a Weyssenhoff fluid satisfying the Frenkel condition, the metric field equations reduce to ordinary Riemannian Einstein equations sourced by an effective fluid containing spin-squared corrections. We derive the effective energy density, radial pressure, and tangential pressure, allowing both isotropic and anisotropic spin correlations. In contrast with Einstein--Cartan theory, the coefficient of the effective spin-spin interaction is not fixed, but depends on the dimensionless quadratic-torsion couplings. In the Einstein--Cartan limit, using the metric definition of the stress-energy tensor, the unpolarized spin contribution gives $w_{\mathrm{spin}}=-1/3$. We then derive the corresponding modified Tolman--Oppenheimer--Volkoff equations and solve them numerically using the DD2 equation of state. For the positive effective spin-spin coupling branch considered here, the torsion correction makes the stellar configurations more compact, lowers the maximum mass, and reduces the binding energy relative to the general-relativistic sequence. For the smooth weak-polarization profiles considered, spin-correlation anisotropy has only a negligible effect on the mass--radius relation.