Abstract
In this present work, we suggest studying neutron star with a conformal coupling by using the analytical expressions of realistic equations of state. The equations of perturbed and nonperturbed metrics, scalar field and the pressure of the matter are derived in order to observe the effects of the conformal coupling on the mass, radius and tidal love number of polar and axial types. The numerical and the analytical analysis show a different comportment of our model from GR by varying the value of the parameters in the model. We showed also for a particular case that the scalar field becomes vanished outside the star which will give us the opportunity to investigate the behaviour tidal love number of our model. Finally, a comparison between the results of our model and the outcome from the signal of gravitational waves, coming from the fusion of binary neutron star, was performed using the universal relations $C$-$\Lambda$.
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