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Stellar structure is investigated within the framework of scalar-tensor gravity. Novel perturbative analytical results are obtained for constant-density stars and for Newtonian polytropes in the quadratic model with coupling function A(Φ) = exp(αΦ+1/2βΦ^2). They are compared to full numerical calculations, and possible applications to main-sequence stars, white dwarfs, and the Chandrasekhar mass are indicated. It is found that Buchdahl's theorem is violated in Brans-Dicke theory for stars with exponentially-decaying density profiles. However, the mass-to-radius ratio M/R tends to the constant-density value in a certain limit. It is observed that for β < 0, there exists a maximum value of η = P0/ρo for constant-density stars, where P0 and ρ0 are the central pressure and density, respectively. It is conjectured that if such a maximum value also exists for other equations of state, and is less than the constant-density maximum value, then knowledge of P/ρ in the centre of a star can be used to constrain β. / Thesis / Master of Science (MSc)

In this work, we review three topics which are relevant on its own but which are also interconnected through the AdS/CFT correspondence: (i) black holes in AdS and its thermodynamics, (ii) nonlinear instability of AdS and (iii) scalar- tensor theory of gravity. Each one of these topics find applications in holography using the above mentioned correspondence. We review the various coordinate systems used to write the AdS metric and discuss the main black holes with AdS asymptotics as well as their thermodynamical properties. We also review current results on linear and nonlinear stability for various spacetimes, presenting a heuristic explanation for the nonlinear instability of AdS. The discussion about alternative theories of gravity is restricted to the case of scalar-tensor theories (Horndeski theories, specially). We study the multipole expansion of the electromagnetic field in the solitonic background of a shift-symmetric scalar-tensor model (up to second order in the scalar field coupling constant with the Gauss-Bonnet term). We find that the multipoles are everywhere regular and finite except for the monopole l = 0, which diverges at the origin of the spacetime coordinates. / Neste trabalho, temos como objetivo fazer uma revisão sobre três temas de grande relevância por si só mas, que também se interligam através da correspondencia AdS/CFT: (i) buracos negros em AdS e sua termodinâmica, (ii) a instabilidade não-linear de AdS e (iii) teorias escalar-tensoriais da gravidade. Cada um destes temas encontram aplicações em holografia usando a correspondencia citada acida. Revisamos as diversas formas de escrever a métrica de AdS e discutimos os principais buracos negros assintóticamentes AdS assim como suas propriedades termodinâmicas. Nós também revisamos os resultados atuais sobre a estabilidade linear e não-linear para diversos espaços-tempos, reproduzindo uma explicação heurísitca sobre a instabilidade não-linear do espaço-tempo AdS. A discussão das teorias alternativas à Relatividade Geral é restrita ao caso das teorias escalar-tensorias da gravidade (a teoria de Horndeski, especialmente). Nós estudamos a expansão multipolar do campo electromagnético em um espaço-tempo que é solução do modelo \"shift-symmetric scalar tensor gravity\" (até segunda ordem na constante de acoplamento do campo escalar com o termo de Gauss-Bonnet) com características solitônicas. Encontramos que os multipolos são regulares e finitos em todo espaço-tempo com exceção do monopolo l = 0, que diverge na origem do sistema de coordenadas.

<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)