Spontaneous scalarization of neutron stars in teleparallel gravity with derivative torsional coupling

Abstract

We study neutron star configurations in a teleparallel gravity model featuring a scalar field coupled to both matter and torsion. In the Einstein frame, the theory includes a derivative coupling between the scalar field and the torsion vector, together with a conformal matter coupling \(A(φ)=\exp(βφ^{2}/2)\). Static and slowly rotating neutron-star solutions are constructed for realistic equations of state, focusing on the APR and MS1 equations of state. Scalarized solutions appear only within a finite range of central densities and correspond to localized deviations from the general-relativistic mass--radius and mass--central-density relations. The onset and extent of scalarization depend on the equation of state and on the strength of the derivative torsional interaction, which can either enhance or suppress scalarization relative to the general-relativistic scalarized branch. At high central densities, scalarization is quenched and the solutions approach the general-relativistic limit, remaining bounded even for strong torsional couplings. No scalarized solutions are found in the absence of matter coupling (\(β=0\)). The normalized scalar charge follows trends consistent with the global mass relations, indicating an intermediate scalarized regime suppressed at high compactness. For slowly rotating stars, the moment of inertia depends systematically on the torsional coupling and the equation of state, with stiffer equations yielding larger values. These results highlight the potential of neutron-star radius and rotational measurements to test teleparallel scalarization scenarios.

Figures (4)

• Figure 1: Properties of NS for $\beta =-4\pi\times 4.8$ using the APR EOS. We show the mass $M$ vs the central energy density $\rho_{c}$ (left panel), the mass $M$ vs the star radius $R$ (middle panel), and the normalized scalar charge $Q$ vs the mass $M$ (right panel). The solid black curves correspond to the GR solutions while the black dashed curvess correspond to the uncoupled case $\xi=0$. The colored solid curves correspond to the values: $\xi=0.5$ (green), $\xi=2.5$ (red) and $\xi=5$ (blue) and $\xi=-0.5$ (pink), $\xi=-2.5$ (orange), $\xi=-5$ (purple).
• Figure 2: Properties of NS for the MSI EOS and $\beta =-4\pi\times 6$ We use the same parameters and colors as in Fig. \ref{['fig:plots_apr']}.
• Figure 3: Effect of varying $\beta$ on the scalarized branch solutions on mass-radius and the charge-mass relations for the APR EOS. The black solide curves is the standard GR solutions while the red curves are the scalarized solutions for $\beta=-4\pi\times 4.8$ (solid for $\xi=0$ and dashed for $\xi=2.5$) and blue curves for $\beta=-4\pi\times 6$ (solid for $\xi=0$ and dashed for $\xi=2.5$).
• Figure 4: The moment of inertia as a function of the mass for APR EOS (left) and MS1 EOS (right) using the same parameters of Fig.\ref{['fig:plots_apr']}