G\"{o}del-type universes in f(R) gravity

The $f(R)$ gravity theories provide an alternative way to explain the current cosmic acceleration without a dark energy matter component. If gravity is governed by a $f(R)$ theory a number of issues should be reexamined in this framework, including the violation of causality problem on nonlocal scale. We examine the question as to whether the $f(R)$ gravity theories permit space-times in which the causality is violated. We show that the field equations of these $f(R)$ gravity theories do not exclude solutions with breakdown of causality for a physically well-motivated perfect-fluid matter content. We demonstrate that every perfect-fluid G\"{o}del-type solution of a generic $f(R)$ gravity satisfying the condition $df/dR > 0$ is necessarily isometric to the G\"odel geometry, and therefore presents violation of causality. This result extends a theorem on G\"{o}del-type models, which has been established in the context of general relativity. We also derive an expression for the critical radius $r_c$ (beyond which the causality is violated) for an arbitrary $f(R)$ theory, making apparent that the violation of causality depends on both the $f(R)$ gravity theory and the matter content. As an illustration, we concretely take a recent $f(R)$ gravity theory that is free from singularities of the Ricci scalar and is cosmologically viable, and show that this theory accommodates noncausal as well as causal G\"odel-type solutions.Comment: 7 pages, V3: Version to appear in Phys. Rev. D (2009), typos corrected, the generality of our main results is emphasized. The illustrative character of a particular theory is also made explici

Gravitational Rainbow

It is shown that unlike Einstein's gravity quadratic gravity produces dispersive photon propagation. The energy-dependent contribution to the deflection of photons passing by the Sun is computed and subsequently the angle at which the visible spectrum would be spread over is plotted as a function of the $R_{\mu\nu}^2-$sector mass

Metric-scalar gravity with torsion and the measurability of the non-minimal coupling

The "measurability" of the non-minimal coupling is discussed by considering the correction to the Newtonian static potential in the semi-classical approach. The coefficient of the "gravitational Darwin term" (GDT) gets redefined by the non-minimal torsion-scalar couplings. Based on a similar analysis of the GDT in the effective field theory approach to non-minimal scalar we conclude that for reasonable values of the couplings the correction is very small.Comment: 10 pages, LaTex. Accepted for publication in Mod. Phys. Lett.

Closed timelike curves and geodesics of Godel-type metrics

It is shown explicitly that when the characteristic vector field that defines a Godel-type metric is also a Killing vector, there always exist closed timelike or null curves in spacetimes described by such a metric. For these geometries, the geodesic curves are also shown to be characterized by a lower dimensional Lorentz force equation for a charged point particle in the relevant Riemannian background. Moreover, two explicit examples are given for which timelike and null geodesics can never be closed.Comment: REVTeX 4, 12 pages, no figures; the Introduction has been rewritten, some minor mistakes corrected, many references adde

Um estudo da estrutura das representações sociais de ensino de ciências de licenciandos em Física

Este trabalho tem como objetivo contribuir com as discussões acerca da reformulação dos cursos de formação de professores, a partir do estudo das representações sociais de ensino de ciências de licenciandos em Física. O delineamento metodológico baseou-se na Teoria das Representações Sociais (Moscovici) e na Teoria do Núcleo Central (Abric). A coleta das informações foi realizada através da aplicação do Teste de Evocação Hierarquizada. Os resultados obtidos foram analisados com base nas técnicas de Bardin e do software EVOC. Através dos quais, identificamos na região nuclear da representação social elementos marcantes do ensino tradicional e da visão baseada em abordagens construtivistas

Um estudo da estrutura das representações sociais de ensino de ciências de licenciandos em Física

Este trabalho tem como objetivo contribuir com as discussões acerca da reformulação dos cursos de formação de professores, a partir do estudo das representações sociais de ensino de ciências de licenciandos em Física. O delineamento metodológico baseou-se na Teoria das Representações Sociais (Moscovici) e na Teoria do Núcleo Central (Abric). A coleta das informações foi realizada através da aplicação do Teste de Evocação Hierarquizada. Os resultados obtidos foram analisados com base nas técnicas de Bardin e do software EVOC. Através dos quais, identificamos na região nuclear da representação social elementos marcantes do ensino tradicional e da visão baseada em abordagens construtivistas

Exact Foldy-Wouthuysen transformation for spin 0 particle in curved space

Up to now, the only known exact Foldy- Wouthuysen transformation (FWT) in curved space is that concerning Dirac particles coupled to static spacetime metrics. Here we construct the exact FWT related to a real spin-0 particle for the aforementioned spacetimes. This exact transformation exists independently of the value of the coupling between the scalar field and gravity. Moreover, the gravitational Darwin term written for the conformal coupling is one third of the relevant term in the fermionic case.Comment: 10 pages, revtex, improved version to appear in Phys. Rev.

General Relativistic Scalar Field Models in the Large

For a class of scalar fields including the massless Klein-Gordon field the general relativistic hyperboloidal initial value problems are equivalent in a certain sense. By using this equivalence and conformal techniques it is proven that the hyperboloidal initial value problem for those scalar fields has an unique solution which is weakly asymptotically flat. For data sufficiently close to data for flat spacetime there exist a smooth future null infinity and a regular future timelike infinity.Comment: 22 pages, latex, AGG 1