Geodesic properties in terms of multipole moments in scalar-tensor theories of gravity

The formalism for describing a metric and the corresponding scalar in terms of multipole moments has recently been developed for scalar-tensor theories. We take advantage of this formalism in order to obtain expressions for the observables that characterise geodesics in terms of the moments. These expressions provide some insight into how the structure of a scalarized compact object affects observables. They can also be used to understand how deviations from general relativity are imprinted on the observables.Comment: 16 page

Approximate Universal Relations for Neutron Stars and Quark Stars

Neutron stars and quark stars are ideal laboratories to study fundamental physics at supra nuclear densities and strong gravitational fields. Astrophysical observables, however, depend strongly on the star's internal structure, which is currently unknown due to uncertainties in the equation of state. Universal relations, however, exist among certain stellar observables that do not depend sensitively on the star's internal structure. One such set of relations is between the star's moment of inertia ($I$), its tidal Love number (Love) and its quadrupole moment ($Q$), the so-called I-Love-Q relations. Similar relations hold among the star's multipole moments, which resemble the well-known black hole no-hair theorems. Universal relations break degeneracies among astrophysical observables, leading to a variety of applications: (i) X-ray measurements of the nuclear matter equation of state, (ii) gravitational wave measurements of the intrinsic spin of inspiraling compact objects, and (iii) gravitational and astrophysical tests of General Relativity that are independent of the equation of state. We here review how the universal relations come about and all the applications that have been devised to date.Comment: 89 pages, 38 figures; review article submitted to Physics Report

Anomalous scaling of a passive scalar advected by the Navier--Stokes velocity field: Two-loop approximation

The field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by a non-Gaussian velocity field with finite correlation time. The velocity is governed by the Navier--Stokes equation, subject to an external random stirring force with the correlation function $\propto \delta(t-t') k^{4-d-2\epsilon}$. It is shown that the scalar field is intermittent already for small $\epsilon$, its structure functions display anomalous scaling behavior, and the corresponding exponents can be systematically calculated as series in $\epsilon$. The practical calculation is accomplished to order $\epsilon^{2}$ (two-loop approximation), including anisotropic sectors. Like for the well-known Kraichnan's rapid-change model, the anomalous scaling results from the existence in the model of composite fields (operators) with negative scaling dimensions, identified with the anomalous exponents. Thus the mechanism of the origin of anomalous scaling appears similar for the Gaussian model with zero correlation time and non-Gaussian model with finite correlation time. It should be emphasized that, in contrast to Gaussian velocity ensembles with finite correlation time, the model and the perturbation theory discussed here are manifestly Galilean covariant. The relevance of these results for the real passive advection, comparison with the Gaussian models and experiments are briefly discussed.Comment: 25 pages, 1 figur

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\u27s 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\u27s coupling parameter. However, the influence of the scalar field is degenerate with uncertainties in the equation of state of the star\u27s 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

Weak lensing in scalar-tensor theories of gravity

This article investigates the signatures of various models of dark energy on weak gravitational lensing, including the complementarity of the linear and non-linear regimes. It investigates quintessence models and their extension to scalar-tensor gravity. The various effects induced by this simplest extension of general relativity are discussed. It is shown that, given the constraints in the Solar System, models such as a quadratic nonminimal coupling do not leave any signatures that can be detected while other models, such as a runaway dilaton, which include attraction toward general relativity can let an imprint of about 10%.Comment: 25 pages, 29 figure

Time evolution of Einstein-Maxwell-scalar black holes after a thermal quench

We employ the holographic quench technique to drive Einstein-Maxwell-scalar (EMs) black holes out of equilibrium and study the real-time dynamics therein. From the fully nonlinear dynamical simulations, a dynamically unstable Reissner-Nordstr$\ddot{\text{o}}$m anti-de Sitter (RN-AdS) black hole can be scalarized spontaneously after an arbitrarily small quench. On the other hand, a dynamically stable scalarized black hole can be descalarized after a quench of sufficient strength. Interestingly, on the way to descalarization, the scalarized black hole behaves like a holographic superfluid, undergoing a dynamical transition from oscillatory to non-oscillatory decay. Such behaviors are related to the spectrums of quasi-normal modes of scalarized black holes, where the dominant mode migrates toward the imaginary axis with increasing quench strength. In addition, due to the $\mathbb Z_{2}$-symmetry preserved by the model, the ground state is degenerate. We find that there exists a threshold for the quench strength that induces a dynamical transition of the gravitational system from one degenerate ground state to the other. Near the threshold, the gravitational system is attracted to an excited state, that is, a RN-AdS black hole with dynamical instability

Dynamical Chameleon Neutron Stars: stability, radial oscillations and scalar radiation in spherical symmetry

Scalar-tensor theories whose phenomenology differs significantly from general relativity on large (e.g. cosmological) scales do not typically pass local experimental tests (e.g. in the solar system) unless they present a suitable "screening mechanism". An example is provided by chameleon screening, whereby the local general relativistic behavior is recovered in high density environments, at least in weak-field and quasi-static configurations. Here, we test the validity of chameleon screening in strong-field and highly relativistic/dynamical conditions, by performing fully non-linear simulations of neutron stars subjected to initial perturbations that cause them to oscillate or even collapse to a black hole. We confirm that screened chameleon stars are stable to sufficiently small radial oscillations, but that the frequency spectrum of the latter shows deviations from the general relativistic predictions. We also calculate the scalar fluxes produced during collapse to a black hole, and comment on their detectability with future gravitational-wave interferometers.Comment: 21 pages, 17 figure

Superradiance -- the 2020 Edition

Superradiance is a radiation enhancement process that involves dissipative systems. With a 60 year-old history, superradiance has played a prominent role in optics, quantum mechanics and especially in relativity and astrophysics. In General Relativity, black-hole superradiance is permitted by the ergoregion, that allows for energy, charge and angular momentum extraction from the vacuum, even at the classical level. Stability of the spacetime is enforced by the event horizon, where negative energy-states are dumped. Black-hole superradiance is intimately connected to the black-hole area theorem, Penrose process, tidal forces, and even Hawking radiation, which can be interpreted as a quantum version of black-hole superradiance. Various mechanisms (as diverse as massive fields, magnetic fields, anti-de Sitter boundaries, nonlinear interactions, etc...) can confine the amplified radiation and give rise to strong instabilities. These "black-hole bombs" have applications in searches of dark matter and of physics beyond the Standard Model, are associated to the threshold of formation of new black hole solutions that evade the no-hair theorems, can be studied in the laboratory by devising analog models of gravity, and might even provide a holographic description of spontaneous symmetry breaking and superfluidity through the gauge-gravity duality. This work is meant to provide a unified picture of this multifaceted subject. We focus on the recent developments in the field, and work out a number of novel examples and applications, ranging from fundamental physics to astrophysics.Comment: 279 pages. Second Edition of the "Lecture Notes in Physics" book by Springer-Verlag. Overall improvement, typos and incorrect statements of Edition 1 are now corrected; new sections were added, reflecting activity in the field. Bounds on ultralight fields are summarized in Table 4, and updated online regularly at https://centra.tecnico.ulisboa.pt/network/grit/ and https://web.uniroma1.it/gmunu