Compact Objects In Relativistic Theories Of Gravity
In this dissertation we discuss several aspects of compact objects, i.e. neutron stars and black holes, in relativistic theories of gravity. We start by studying the role of nuclear physics (encoded in the so-called equation of state) in determining the properties of neutron stars in general relativity. We show that low-mass neutron stars are potentially useful astrophysical laboratories that can be used to constrain the properties of the equation of state. More specifically, we show that various bulk properties of these objects, such as their quadrupole moment and tidal deformability, are tightly correlated. Next, we develop a formalism that aims to capture how generic modifications from general relativity affect the structure of neutron stars, as predicted by a broad class of gravity theories, in the spirit of the parametrized post-Newtonian formalism (ppn). Our "post-Tolman-Oppenheimer-Volkoff" formalism provides a toolbox to study both stellar structure and the interior/exterior geometries of static, spherically symmetric relativistic stars. We also apply the formalism to parametrize deviations from general relativity in various astrophysical observables related with neutron stars, including surface redshift, apparent radius, Eddington luminosity. We then turn our attention to what is arguably the most well-motivated and well-investigated generalization of general relativity: scalar-tensor theory. We start by considering theories where gravity is mediated by a single extra scalar degree of freedom (in addition to the metric tensor). An interesting class of scalar-tensor theories passes all experimental tests in the weak-field regime of gravity, yet considerably deviates from general relativity in the strong-field regime in the presence of matter. A comassumption in modeling neutron stars is that the pressure within these object is spatially isotropic. We relax this assumption and examine how pressure anisotropy affects the mass, radius and moment of inertia of slowly rotating neutron stars, both in general relativity and in scalar-tensor gravity. We show that a sufficient amount of pressure anisotropy results in neutron star models whose properties in scalar-tensor theory deviate significantly from their general relativistic counterparts. Moreover, the presence of anisotropy allows these deviations to be considerable even for values of the theory's coupling parameter for which neutron stars in scalar-tensor theory would be otherwise indistinguishable from those in general relativity. Within scalar-tensor theory we also investigate the effects of the scalar field on the crustal torsional oscillations of neutron stars, which have been associated to quasi-periodic oscillations in the x-ray spectra in the aftermath of giant flares. We show that the presence of the scalar field has an influence on the thickness of the stellar crust, and investigate how it affects the oscillation frequencies. Deviations from the predictions of general relativity can be large for certain values of the theory's coupling parameter. However, the influence of the scalar field is degenerate with uncertainties in the equation of state of the star's crust and microphysics effects (electron screening) for values of the coupling alloby binary pulsar observations. We also derive the stellar structure equations for slowly-rotating neutron stars in a broader class of scalar-tensor theories in which matter and scalar field are coupled through the so-called disformal coupling. We study in great detail how the disformal coupling affects the structure of neutron stars, and we investigate the existence of universal (equation of state-independent) relations connecting the stellar compactness and moment of inertia. In particular, we find that these universal relations can deviate considerably from the predictions of general relativity. We then study neutron stars in tensor-multi-scalar theories, focusing on a particular model with two scalar degrees of freedom. We start with a detailed exposition of the formulation of this theory and, in particular, we show that it can be transformed into a scalar-tensor theory for a single complex-valued field with non-trivial kinetic term in the action. This theory possesses a larger parameter space in comparison with the single-field scalar-tensor gravity, and certain combinations of these parameters are currently unconstrained by observations. After a discussion of the formal aspects of the theory, we derive the stellar structure equations for slowly-rotating relativistic stars. Our numerical results reveal that the theory possesses a very rich phenomenology. Additionally, we present the 3+1 decomposition of the field equations, a fundamental requirement to perform numerical relativity evolutions. Finally, we consider the most general scalar-tensor theory that yields second-order field equations: horndeski gravity. We first study black hole solutions, and we generalize existing no-hair theorems to the case of slowly rotating black holes. Only a subclass of horndeski gravity (namely einstein-dilaton-gauss-bonnet gravity) supports asymptotically flat black holes with nontrivial scalar field configurations in first perturbative order in rotation. We also explore the existence of neutron stars in horndeski gravity. We show that certain subclasses of the theory do not admit neutron star solutions. For the subclasses of the theory were these solutions exist, we study the properties of slowly rotating neutron stars, and obtain novel equation of state-independent relations connecting their compactness and moment of inertia.
Black Holes, Equation Of State, Gravitation, Neutron Stars, Scalar-Tensor Gravity, Tests Of Gravity, Physics
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