<p>The properties of neutron stars and black holes are investigated within a class of alternative theories of gravity known as Scalar-Tensor theories, which extend General Relativity by introducing additional light scalar fields to mediate the gravitational interaction.</p> <p>It has been known since 1993 that neutron stars in certain Scalar-Tensor theories may undergo ‘scalarization’ phase transitions. The Weak Central Coupling (WCC) expansion is introduced for the purpose of describing scalarization in a perturbative manner, and the leading-order WCC coefficients are calculated analytically for constant-density stars. Such stars are found to scalarize, and the critical value of the quadratic scalar-matter coupling parameter β_s = −4.329 for the phase transition is found to be similar to that of more realistic neutron star models.</p> <p>The influence of cosmological and galactic effects on the structure of an otherwise isolated black hole in Scalar-Tensor gravity may be described by incorporating the Miracle Hair Growth Formula discovered by Jacobson in 1999, a perturbative black hole solution with scalar hair induced by time-dependent boundary conditions at spatial infinity. It is found that a double-black-hole binary (DBHB) subject to these boundary conditions is inadequately described by the Eardley Lagrangian and emits scalar dipole radiation.</p> <p>Combining this result with the absence of observable dipole radiation from quasar OJ287 (whose quasi-periodic ‘outbursts’ are consistent with the predictions of a general-relativistic DBHB model at the 6% level) yields the bound |φ/Mpl| < (16 days)^-1 on the cosmological time variation of canonically-normalized light (m < 10⁻²³ eV) scalar fields at redshift z ∼ 0.3.</p> / Doctor of Philosophy (PhD)

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-13T14:39:21Z No. of bitstreams: 1 arquivototal.pdf: 851323 bytes, checksum: 599a5da8bbbe70ff2f4ba121890878e2 (MD5) / Made available in DSpace on 2017-09-13T14:39:21Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 851323 bytes, checksum: 599a5da8bbbe70ff2f4ba121890878e2 (MD5) Previous issue date: 2014-07-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this cool thesis, we consider an approach to Brans-Dicke theory of gravity in which the scalar eld has a geometrical nature. By postulating the Palatini variation, we nd out that the role played by the scalar eld consists in turning the space-time geometry into a Weyl integrable manifold. This procedure leads to a scalar-tensor theory that di ers from the original Brans-Dicke theory in many aspects and presents some new features. We also consider the Weyl integrable geometry to investigate gravity in (2+1)-dimensions. We show that, in addition to leading to a Newtonian limit, WIST in (2+1) dimensions presents some interesting properties that are not shared by Einstein theory, such as geodesic deviation between particles in a dust distribution. Finally, taking advantage of the duality between the geometrical scalar-tensor theory and general relativity coupled with a massless scalar eld we study naked singularities and wormholes. / Esta tese trata de tópicos relacionados às teorias escalares-tensoriais e a geometria de Weyl integrável. Nossa abordagem será no sentido de indicar a geometria de Weyl integr ável como sendo um ambiente natural para a introdução de teorias escalares-tensorias. Nossa discussão será em torno da teoria de Brans-Dicke, considerada o protótipo das teorias escalares tensoriais, no entanto a discussão é facilmente estendida para essas versões mais gerais. Fazemos isso em dois momentos. Primeiro, indicando, no âmbito da teoria de Brans-Dicke, que na estrutura geométrica e de campos adotadas pela teoria existe uma relação estreita com a geometria de Weyl, inclusive associando o efeito descrito na literatura como "quinta força"(que violaria o princípio de equivalência) com o movimento geodésico da geometria de Weyl integrável, reformulando o postulado geodésico. E, num segundo momento, usando o método variacional de Palatini, acabamos por formular uma nova teoria escalar-tensorial, agora com ingredientes completamente geométricos, ambientada numa geometria de Weyl integrável. Estudamos ainda soluções no vazio do problema estático de uma distribuição de massa esfericamente simétrica, onde surgem objetos de interesse astrofísico como singularidades nuas e buracos de minhoca. Também formulamos a teoria conhecida por WIST (Weyl Integrable Spacetimes) em (2 + 1)D, o que resulta numa teoria consistente, não sofrendo das falhas associadas à teoria da relatividade geral nessa dimensionalidade

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-18T11:29:37Z No. of bitstreams: 1 arquivototal.pdf: 1956067 bytes, checksum: 845c3d0cd5113c8498d955af9cdcd907 (MD5) / Made available in DSpace on 2017-09-18T11:29:37Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1956067 bytes, checksum: 845c3d0cd5113c8498d955af9cdcd907 (MD5) Previous issue date: 2016-09-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis, we deal with a particular geometric scalar tensor theory, which is a version of the Brans-Dicke gravitation, formulated in aWeyl integrable space-time. This formulation is done using the Palatini's variation procedure. The main point of our work is to perform two particular applications of the geometrical Brans-Dicke theory. The rst one is the study of geometric fase transition phenomena, that's related to a continuous change in the space-time structure of the universe from a Riemann's geometry to a Weyl's geometry, or in the inverse sense, from Weyl's geometry to Riemann's geometry. This phenomena seems to take place when the universe starts to expand in a accelerated rate. The second one is the investigation of classical and quantum behaviour of a anisotropic n-dimensional universe . To nd solutions that display the dynamical compacti cation of non observed extra dimensions is the main motivation to study such universe. / Nesta tese, reapresentamos uma teoria escalar tensorial geométrica, que é uma versão da gravitação de Brans-Dicke formulada em um espaço-tempo de Weyl integrável. Com esta teoria fazemos duas aplicações especí cas. Uma delas para o estudo de um fenômeno, que chamamos de transição de fase geométrica, uma mudança contínua na estrutura geom étrica do espaço-tempo. Este fenômeno parece ocorrer quando o universo se expande aceleradamente. A segunda aplicação reside no estudo clássico e quântico do comportamento de um modelo de universo n-dimensional anisotrópico. A motivação para esta investigação é a busca de soluções que exibem o compactação dinâmica das dimensões extras, que não são observadas.

Cette thèse porte sur la gravitation et certains de ses liens avec la théorie des champs. Le point de départ de cette recherche a été l’étude de la limite newtonienne de la relativité générale. Très vite, notre intérêt s’est porté sur l’effet du temps retardé et son rôle dans l’absence d’aberration. Ce manque d’aberration est la raison pour laquelle la force pointe dans la direction instantanée (extrapolée) pour des sources sans accélération, malgré la vitesse finie de la gravitation (c’est aussi le cas pour l’électromagnétisme). Ceci nous a conduit à calculer le champ résultant entre deux masses accélérées avec la présence d’aberration. Nous avons en particulier considéré le mouvement de deux masses de telle façon que la force totale de Newton à une position s’annule alors que les effets du temps retardé soient bien différents de zéro. Nous avons pu calculer ces derniers et proposer deux situations où ils pourraient être observés dans le futur. L’étude de la linéarisation de la relativité générale a naturellement porté notre intérêt sur la physique du graviton, la version quantifiée de la théorie classique linéaire. Plusieurs travaux sur l’impossibilité d’observer directement ce graviton [1,2] ainsi que des expériences de pensée sur la possibilité de le quantifier ou non [3] ont piqué notre curiosité. C’est ce qui a lancé la recherche de la section efficace (et du potentiel) dans le cas d’une diffusion gravitationnelle sur une particule initialement dans une superposition spatiale. En parallèle de ces recherches, des discussions avec mon collègue Kévin Nguyen et la lecture de son article [4], ont attiré mon attention sur le problème de la constante cosmologique et l’élégante solution proposée. Cette dernière est basée sur l’ajout d’un scalaire couplé non minimalement avec la gravité et permet d’expliquer la valeur minuscule de la constante cosmologique par certains très petits paramètres du champ scalaire. Leur solution était cependant encore très théorique, car elle n’était valable que dans un univers sans matière. Nous avons donc analysé l’effet de la matière sur l’évolution du champ scalaire et montré que dans une partie de l’espace des paramètres, la théorie considérée résolvait le problème de la constante cosmologique tout en restant indistinguable de la relativité générale. / This thesis concerns gravitation and some of its connections with field theory. The starting point of this research was the study of the Newtonian limit of general relativity. Our interest was focused on the effect of retarded time and its role in the absence of aberration. Lack of aberration is the reason why the gravitational force points in the instantaneous (extrapolated) direction for unaccelerated sources, despite the finite speed of propagation of gravity (this also holds true for electromagnetism). Naturally this led us to compute the resulting gravitational field of accelerating masses, where aberration is not absent. In particular, we considered the motion of two masses such that their total Newtonian force at a position vanished but the retarded gravitational effects were non-zero. We were able to calculate these retarded effects and to propose two situations where they could be observed in the future. The study of the linearization of general relativity naturally arouse our interest toward the physics of gravitons, the quantized version of the linear classical theory. In particular, there has been much thought and literature on the impossibility of directly observing a graviton [1, 2] as well as thought experiments on the possibility of quantizing gravity or not [3]. This led to the calculation of the cross section (and gravitational potential) in the case of the gravitational scattering off a massive particle that is in a spatially non-local quantum superposition. In parallel with this research, some discussions with my colleague Kévin Nguyen about his article [4] on the problem of the cosmological constant, focussed my interest on this problem and the elegant solution proposed. The solution is based on the addition of a nonminimally coupled scalar and makes it possible to explain the tiny value of the cosmological constant through some small parameters of the scalar field. The solution is however very theoretical as it was only done in a matter free universe. We therefore examined at the effect of different kinds of matter on the evolution of the scalar field. We show that in one part of the parameter space, the theory we considered resolved the cosmological constant problem while being indistinguishable from general relativity.

Cette thèse est consacrée au problème d’évolution des théories de gravité modifiée : après avoir rappelé ce qu’il en est pour la Relativité Générale (RG), nous exposons le formalisme n + 1 des théories ƒ(R), Brans-Dicke et tenseur-scalaire et redémontrons un résultat connu : le problème de Cauchy est bien posé pour ces théories, et les équations de contrainte se réduisent à celles de la RG avec un champ de matière. Puis nous effectuons la même décomposition n + 1 pour les théories de Lovelock et, ce qui est nouveau, ƒ(Lovelock). Nous étudions ensuite les équations de contrainte des théories de Lovelock et montrons qu’elles sont, dans le cas conformément plat et symétrique en temps, la prescription d’une somme de σk-courbures. Afin de résoudre cette équation de prescription, nous introduisons une nouvelle famille de polynômes semi-symétriques homogènes et développons des résultats de concavité pour ces polynômes. Nous énonçons une conjecture qui, si elle était avérée, nous permettrait de résoudre l’équation de prescription dans de nombreux cas : ∀ P;Q ∈ ℝ[X], avec deg P = deg Q = p, P et Q sont scindés => p ∑ k=0 P(k) Q(p-k) est scindé / This thesis is devoted to the evolution problem for modified gravity theories. After having explained this problem for General Relativity (GR), we present the n + 1 formalism for ƒ(R) theories, Brans-Dicke and scalar-tensor theories. We recall a known result: the Cauchy problem for these theories is well-posed, and the constraint equations are reduced to those of GR with a matter field. Then we proceed to the same n+1 decomposition for Lovelock and ƒ(Lovelock) theories, the latter being an original result. We show that in the locally conformally flat timesymmetric case, they can be written as the prescription of a sum of σk-curvatures. In order to solve the prescription equation, we introduce a new family of homogeneous semisymmetric polynomials and prove some concavity results for those polynomials. We express the following conjecture: if this is true, we are able to solve the prescription equation in many cases. ∀ P;Q ∈ ℝ[X], avec deg P = deg Q = p, P and Q are real-rooted => p ∑ k=0 P(k) Q(p-k) is real-rooted: