Spherically symmetric spacetimes in f(R) gravity theories

We study both analytically and numerically the gravitational fields of stars in f(R) gravity theories. We derive the generalized Tolman-Oppenheimer-Volkov equations for these theories and show that in metric f(R) models the Parameterized Post-Newtonian parameter $\gamma_{\rm PPN} = 1/2$ is a robust outcome for a large class of boundary conditions set at the center of the star. This result is also unchanged by introduction of dark matter in the Solar System. We find also a class of solutions with $\gamma_{\rm PPN} \approx 1$ in the metric $f(R)=R-\mu^4/R$ model, but these solutions turn out to be unstable and decay in time. On the other hand, the Palatini version of the theory is found to satisfy the Solar System constraints. We also consider compact stars in the Palatini formalism, and show that these models are not inconsistent with polytropic equations of state. Finally, we comment on the equivalence between f(R) gravity and scalar-tensor theories and show that many interesting Palatini f(R) gravity models can not be understood as a limiting case of a Jordan-Brans-Dicke theory with $\omega \to -3/2$.Comment: Published version, 12 pages, 7 figure

Equilibrium hydrostatic equation and Newtonian limit of the singular f(R) gravity

We derive the equilibrium hydrostatic equation of a spherical star for any gravitational Lagrangian density of the form $L=\sqrt{-g}f(R)$. The Palatini variational principle for the Helmholtz Lagrangian in the Einstein gauge is used to obtain the field equations in this gauge. The equilibrium hydrostatic equation is obtained and is used to study the Newtonian limit for $f(R)=R-\frac{a^{2}}{3R}$. The same procedure is carried out for the more generally case $f(R)=R-\frac{1}{n+2}\frac{a^{n+1}}{R^{n}}$ giving a good Newtonian limit.Comment: Revised version, to appear in Classical and Quantum Gravity

Cosmological perturbations in Palatini modified gravity

Two approaches to the study of cosmological density perturbations in modified theories of Palatini gravity have recently been discussed. These utilise, respectively, a generalisation of Birkhoff's theorem and a direct linearization of the gravitational field equations. In this paper these approaches are compared and contrasted. The general form of the gravitational lagrangian for which the two frameworks yield identical results in the long-wavelength limit is derived. This class of models includes the case where the lagrangian is a power-law of the Ricci curvature scalar. The evolution of density perturbations in theories of the type $f(R)=R-c /R^ b$ is investigated numerically. It is found that the results obtained by the two methods are in good agreement on sufficiently large scales when the values of the parameters (b,c) are consistent with current observational constraints. However, this agreement becomes progressively poorer for models that differ significantly from the standard concordance model and as smaller scales are considered

Curvature singularities, tidal forces and the viability of Palatini f(R) gravity

In a previous paper we showed that static spherically symmetric objects which, in the vicinity of their surface, are well-described by a polytropic equation of state with 3/2<Gamma<2 exhibit a curvature singularity in Palatini f(R) gravity. We argued that this casts serious doubt on the validity of Palatini f(R) gravity as a viable alternative to General Relativity. In the present paper we further investigate this characteristic of Palatini f(R) gravity in order to clarify its physical interpretation and consequences.Comment: 15 pages. CQG in press. Part of the material moved to an appendix, discussion on the meV scale predictions of Palatini f(R) gravity adde

Kicking the Rugby Ball: Perturbations of 6D Gauged Chiral Supergravity

We analyze the axially-symmetric scalar perturbations of 6D chiral gauged supergravity compactified on the general warped geometries in the presence of two source branes. We find all of the conical geometries are marginally stable for normalizable perturbations (in disagreement with some recent calculations) and the nonconical for regular perturbations, even though none of them are supersymmetric (apart from the trivial Salam-Sezgin solution, for which there are no source branes). The marginal direction is the one whose presence is required by the classical scaling property of the field equations, and all other modes have positive squared mass. In the special case of the conical solutions, including (but not restricted to) the unwarped `rugby-ball' solutions, we find closed-form expressions for the mode functions in terms of Legendre and Hypergeometric functions. In so doing we show how to match the asymptotic near-brane form for the solution to the physics of the source branes, and thereby how to physically interpret perturbations which can be singular at the brane positions.Comment: 21 pages + appendices, references adde

The phase space view of f(R) gravity

We study the geometry of the phase space of spatially flat Friedmann-Lemaitre-Robertson-Walker models in f(R) gravity, for a general form of the function f(R). The equilibrium points (de Sitter spaces) and their stability are discussed, and a comparison is made with the phase space of the equivalent scalar-tensor theory. New effective Lagrangians and Hamiltonians are also presented.Comment: 14 pages, 2 figures, published in Classical and Quantum Gravity; references adde

New distributional data on Geastrum (Geastraceae, Basidiomycota) from Brazil

[EN] (New distributional data on Geastrum (Geastraceae, Basidiomycota) from Brazil). Th e data presented in this article are the results of fi eld collections and the analysis of fungal specimens deposited in the URM Herbarium. Th e fi eld trips were carried out in four Atlantic Forest remnants in the state of Pernambuco, between June 2008 and May 2009. Th e revision of specimens housed in the URM was restricted to the Brazilian exsiccatae. Geastrum specimens were examined macro- and microscopically following the traditional methodology used in the group. Geastrum javanicum and G. lloydianum are new records from the Northeastern Region of Brazil. Eight species are new records from the following states: Pará (G. fi mbriatum), Ceará (G. lloydianum), Paraíba (G. fi mbriatum, G. javanicum, G. schweinitzii and G. entomophilum), Pernambuco (G. lageniforme and G. triplex) and Rio de Janeiro (G. javanicum). In this article we present full descriptions for ten species of Geastrum with pictures and an identifi cation key.[POR] (Novos dados de distribuição de Geastrum (Geastraceae, Basidiomycota) no Brasil). Os dados apresentados neste artigo são resultados de coletas feitas em campo e análise de espécimes fúngicos depositados no Herbário URM. As coletas foram realizadas em quatro remanescentes de mata atlântica no estado de Pernambuco, entre junho/2008 e maio/2009. A revisão de espécimes depositados no URM foi restrita a exsicatas brasileiras. Os espécimes de Geastrum foram examinados macro e microscopicamente segundo a metodologia tradicional do grupo. Geastrum javanicum e G. lloydianum são novos registros para a região Nordeste do Brasil. Oito espécies são novas ocorrências para os seguintes estados: Pará (G. fi mbriatum), Ceará (G. lloydianum), Paraíba (G. fi mbriatum, G. javanicum, G. schweinitzii e G. entomophilum), Pernambuco (G. lageniforme e G. triplex) e Rio de Janeiro (G. javanicum). Apresentamos neste artigo dez descrições completas de espécies de Geastrum, além de fotos das espécies e uma chave de identifi cação.Peer reviewe