Numerical study of the properties of compact objects in general relativity and scalar-tensor theories

In this work we present a detailed study of magnetised neutron stars in general relativity and scalar-tensor theories. First, we carry out a study of the parameter space considering the two extreme geometries of purely toroidal and purely poloidal magnetic fields, varying both the strength of the magnetic field and the intensity of scalarisation. We compare our results with magnetised general-relativistic solutions and unmagnetised scalarised solutions, showing how the mutual interplay between magnetic and scalar fields affect the magnetic and the scalarisation properties of neutron stars. Then, we focus our attention to their magnetic deformation, exploring how the scalar field affects the emission of continuous gravitational waves. In this regard, we present a study of magnetised neutron stars for various realistic equations of state considered viable by observations and nuclear physics constraints, showing that it is possible to find simple relations between the magnetic deformation of a neutron star, its mass, and its radius. Such relations are quasi-universal, meaning that they are mostly independent from the equation of state of the neutron star. Thanks to their formulation in terms of potentially observable quantities, as we discuss, our results could help to constrain the magnetic properties of the neutron stars interior and to better assess the detectability of continuous gravitational waves by isolated neutron stars, without knowing their equation of state. These results are derived both in general relativity and in scalar-tensor theories, in this case by also considering the scalar charge. We show that even in this case, general relations that account for deviations from general relativity still hold, which could potentially be used to set constraints on the gravitational theory. Moreover, we show how the quasi-universal relations we find can be used to assess the detectability of continuous gravitational waves from pulsars in the Galaxy by gravitational waves detectors. Finally, we propose a novel way to test deviations from general relativity in the vicinity of accreting neutron stars, through the use of the Fe Ka fluorescent line at 6.4 keV. In fact, we show how the presence of a scalar field changes the expected line shape with respect to general relativity, revealing that even if those changes are in general of the order of a few percent, they are potentially observable with the next generation of X-ray satellites.