Neutron Stars in Scalar Torsion Theories with Nonminimal Coupling

Abstract

We study the existence and structure of static and slowly rotating neutron stars (NSs) in a particular truncation of scalar torsion theory with a scalar field $ \phi $ non-minimally coupled to the torsion scalar, and a potential of the form $ V(\phi)=-\mu^2\phi^2/2 +\lambda \phi^4 /4 $. We derive the hydrostatic equilibrium equations in the static case and solve them numerically for both interior and exterior regions using the appropriate boundary conditions near the center and far from the star. We plot the radial profiles of the metric functions and the scalar field as well as the mass-radius diagram of the star employing a set of four different realistic equations of state (EoS). Our findings show a high degree of compatibility with the observational constraints of the GW170817 event and indicate a maximum mass $2.37M_{\odot}$ obtained with the BSk21 EoS for a coupling parameter $ \xi=0.25 $. We extend our analysis to include slow rotation, and determine the relation between the star's moment of inertia and its mass. We also show that the universality relation of the two forms of the normalized moment of inertia continue to hold in scalar torsion theory with non minimal coupling.