Axial perturbations of neutron stars with shift symmetric conformal coupling

In this present work, the axial quasi-normal modes of neutron stars, with a shift symmetric conformal coupling, are studied for different realistic equations of state. First, we derive the background equations in static and spherically symmetric spacetime and then we solve them numerically by taking into account the continuity and regularity conditions. Second, we extend our calculus to the perturbed level where we derive the equations of motion as well as the ghost and Laplacian instability. We find that the proposed model is free from these instabilities everywhere. We find also that the variation of the quasi-normal modes is affected by the conformal coupling where the deviation from general relativity is observed. Finally, with this motivation, we fit our numerical result with universal relations for axial quasi-normal modes using five type of realistic equations of state. The universality of the scaled frequency and damping time in terms of the compactness in this model is confirmed in this model.