On the linear and weak-field limits of scalar-tensor theories of gravity

The linear approximation of scalar-tensor theories of gravity is obtained in the physical (Jordan) frame under the 4+0 (covariant) and 3+1 formalisms. Then the weak-field limit is analyzed and the conditions leading to significant deviations of the $1/r^{2}$ Newton's law of gravitation are discussed. Finally, the scalarization effects induced by these theories in extended objects are confronted within the weak-field limit.Comment: 12 pages in revtex4-twocolumn format; submitted to Phys.Rev.

Obstructions towards a generalization of no-hair theorems: I. Scalar clouds around Kerr black holes

We show that the integral method used to prove the no-hair theorem for Black Holes (BH's) in spherically symmetric and static spacetimes within the framework of general relativity with matter composed by a complex-valued scalar-field does not lead to a straightforward conclusion about the absence of hair in the stationary and rotating (axisymmetric) scenario. We argue that such a failure can be used to justify in a simple and heuristic way the existence of non-trivial boson clouds or hair found numerically by Herdeiro and Radu [1,2] and analytically by Hod in the test field limit [3-5]. This is due to the presence of a contribution that is negative when rotation exists which allows for an integral to vanish even when a non-trivial boson hair is present. The presence of such a negative contribution that depends on the rotation properties of the BH is perfectly correlated with the eigenvalue problem associated with the boson-field equation. Conversely, when the rotation is absent the integral turns to be composed only by non negative (i.e. positive semidefinite) terms and thus the only way it can vanish is when the hair is completely absent. This analysis poses serious challenges and obstructions towards the elaboration of no-hair theorems for more general spacetimes endowed with a BH region even when including matter fields that obey the energy conditions. Thus rotating boson stars, if collapsed, may lead indeed to a new type of rotating BH, like the ones found in [1,2]. In order to achieve this analysis we solve numerically the eigenvalue problem for the boson field in the Kerr-BH background by imposing rigorous regularity conditions at the BH horizon for the non-extremal case ($0<a<M$) which include the near extremal one in the limit $M\rightarrow a$, as well as the small BH limit $M\rightarrow a\rightarrow 0$.Comment: 17 pages, 9 figures, 4 table

Cosmic acceleration in asymptotically Ricci flat Universe

We analyze the evolution of a Friedmann-Robertson-Walker spacetime within the framework of $f(R)$ metric gravity using an exponential model. We show that $f(R)$ gravity may lead to a vanishing effective cosmological constant in the far future (i.e. $R\rightarrow 0$) and yet produce a transient accelerated expansion at present time with a potentially viable cosmological history. This is in contrast with several $f(R)$ models which, while viable, produce in general a non-vanishing effective cosmological constant asymptotically in time ($R\rightarrow 4\Lambda_{\rm eff}$). We also show that relativistic {stars in asymptotically flat spacetimes can be supported within this framework without encountering any singularity, notably in the Ricci scalar $R$.Comment: 12 pages, 18 figures in 9 panel

Has cosmological dark matter been observed?

There are many indications that ordinary matter represents only a tiny fraction of the matter content of the Universe, with the remainder assumed to consist of some different type of matter, which, for various reasons must be nonluminous (dark matter). Among these indications are the inflationary scenarios which predicts that the average energy density of the Universe coincides with the so called critical value (for which the expansion never stops but the rate of expansion approaches zero at very late times). At the same time it is known (from the predictions of Big Bang nucleosynthesis on the abundances of the light elements, other than Helium) that the baryonic energy density (ordinary matter) must represent ($1.5\pm 0.5)h^{-2}$ \% (where $h$ is the Hubble constant in units of 100 km s$^{-1}$Mpc$^{-1}$) of this critical value \cite{Copi,OstStein}. We present here evidence supporting the model in which the rest of the energy density corresponds to a scalar field, which can be observed, however indirectly, in the oscillation of the effective gravitational constant, and manifests itself in the known periodicity of the number distribution of galaxies \cite{Broad,Szalay}. We analyze this model numerically and show that, the requirement that the model satisfy the bounds of light element abundances in the Universe, as predicted by Big Bang nucleosynthesis, yields a specific value for the red-shift-galactic-count oscillation amplitude compatible with that required to explain the oscillations described above \cite{hill,CritStein}, and, furthermore, yields a value for the age of the Universe compatible with standard bounds \cite{OstStein}.Comment: Latex file 15 pages with no figures. Please contact M.Salgado for figures. This paper was submitted the 4 June as a letter for publication in Natur

Cosmology in f(R) exponential gravity

Using an approach that treats the Ricci scalar itself as a degree of freedom, we analyze the cosmological evolution within an f(R) model that has been proposed recently (exponential gravity) and that can be viable for explaining the accelerated expansion and other features of the Universe. This approach differs from the usual scalar-tensor method and, among other things, it spares us from dealing with unnecessary discussions about frames. It also leads to a simple system of equations which is particularly suited for a numerical analysis.Comment: 8 pages (no page numbers), 5 figures (10 panels). Prepared for the Proceedings of Relativity and Gravitation: 100 years after Einstein in Prague, Prague, 25-29 June, 201

Scalar hairy black holes and scalarons in the isolated horizons formalism

The Isolated Horizons (IH) formalism, together with a simple phenomenological model for colored black holes has been used to predict non-trivial formulae that relate the ADM mass of the solitons and hairy Black Holes of Gravity-Matter system on the one hand, and several horizon properties of the black holes in the other. In this article, the IH formalism is tested numerically for spherically symmetric solutions to an Einstein-Higgs system where hairy black holes were recently found to exist. It is shown that the mass formulae still hold and that, by appropriately extending the current model, one can account for the behavior of the horizon properties of these new solutions. An empirical formula that approximates the ADM mass of hairy solutions is put forward, and some of its properties are analyzed.Comment: 17 pages, 10 figures; revtex style; figures added; text updated to match the published pape

The initial value problem of scalar-tensor theories of gravity

The initial value problem of scalar-tensor theories of gravity (STT) is analyzed in the physical (Jordan) frame using a 3+1 decomposition of spacetime. A first order strongly hyperbolic system is obtained for which the well posedness of the Cauchy problem can be established. We provide two simple applications of the 3+1 system of equations: one for static and spherically symmetric spacetimes which allows the construction of unstable initial data (compact objects) for which a further black hole formation and scalar gravitational wave emission can be analyzed, and another application is for homogeneous and isotropic spacetimes that permits to study the dynamics of the Universe in the framework of STT.Comment: 12 pages; RevTex; Published in the Proceedings of the VII Mexican School on Gravitation and Mathematical Physic

About matter and dark-energy domination eras in R^n gravity or lack thereof

We provide further numerical evidence which shows that R^n models in f(R) metric gravity whether produces a late time acceleration in the Universe or a matter domination era (usually a transient one) but not both. Our results confirm the findings of Amendola et al. (2007), but using a different approach that avoids the mapping to scalar-tensor theories of gravity, and therefore, dispense us from any discussion or debate about frames (Einstein vs Jordan) which are endemic in this subject. This class of models has been used extensively in the literature as an alternative to the dark energy, but should be considered ruled out for being inconsistent with observations. Finally, we discuss a caveat in the analysis by Faraoni (2011), which was used to further constrain these models by using a chameleon mechanism.Comment: 6 pages, 6 figures in 2 panels. Accepted for publication in Phys. Rev.

The Einstein-Maxwell system in 3+1 form and initial data for multiple charged black holes

We consider the Einstein-Maxwell system as a Cauchy initial value problem taking the electric and magnetic fields as independent variables. Maxwell's equations in curved spacetimes are derived in detail using a 3+1 formalism and their hyperbolic properties are analyzed, showing that the resulting system is symmetric hyperbolic. We also focus on the problem of finding initial data for multiple charged black holes assuming time-symmetric initial data and using a puncture-like method to solve the Hamiltonian and the Gauss constraints. We study the behavior of the resulting initial data families, and show that previous results in this direction can be obtained as particular cases of our approach.Comment: 20 pages, 6 figures, some typos fixed and references adde

f(R) Cosmology revisited

We consider a class of metric f(R) modified gravity theories, analyze them in the context of a Friedmann-Robertson-Walker cosmology and confront the results with some of the known constraints imposed by observations. In particular, we focus in correctly reproducing the matter and effective cosmological constant eras, the age of the Universe, and supernovae data. Our analysis differs in many respects from previous studies. First, we avoid any transformation to a scalar-tensor theory in order to be exempted of any potential pathologies (e.g. multivalued scalar potentials) and also to evade any unnecessary discussion regarding frames (i.e. Einstein vs Jordan). Second, based on a robust approach, we recast the cosmology equations as an initial value problem subject to a modified Hamiltonian constraint. Third, we solve the equations numerically where the Ricci scalar itself is one of the variables, and use the constraint equation to monitor the accuracy of the solutions. We compute the "equation of state" (EOS) associated with the modifications of gravity using several inequivalent definitions that have been proposed in the past and analyze it in detail. We argue that one of these definitions has the best features. In particular, we present the EOS around the so called "phantom divide" boundary and compare it with previous findings.Comment: 35 pages; 33 figures; revte