Boundary Term in Metric f(R) Gravity: Field Equations in the Metric Formalism

The main goal of this paper is to get in a straightforward form the field equations in metric f(R) gravity, using elementary variational principles and adding a boundary term in the action, instead of the usual treatment in an equivalent scalar-tensor approach. We start with a brief review of the Einstein-Hilbert action, together with the Gibbons-York-Hawking boundary term, which is mentioned in some literature, but is generally missing. Next we present in detail the field equations in metric f(R) gravity, including the discussion about boundaries, and we compare with the Gibbons-York-Hawking term in General Relativity. We notice that this boundary term is necessary in order to have a well defined extremal action principle under metric variation.Comment: 12 pages, title changes by referee recommendation. Accepted for publication in General Relativity and Gravitation. Matches with the accepted versio

Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length

The (D+1)-dimensional $(\beta,\beta')$-two-parameter Lorentz-covariant deformed algebra introduced by Quesne and Tkachuk [C. Quesne and V. M. Tkachuk, J. Phys. A: Math. Gen. \textbf {39}, 10909 (2006).], leads to a nonzero minimal uncertainty in position (minimal length). The Klein-Gordon equation in a (3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where $\beta'=2\beta$ up to first order over deformation parameter $\beta$. It is shown that the modified Klein-Gordon equation which contains fourth-order derivative of the wave function describes two massive particles with different masses. We have shown that physically acceptable mass states can only exist for $\beta<\frac{1}{8m^{2}c^{2}}$ which leads to an isotropic minimal length in the interval $10^{-17}m<(\bigtriangleup X^{i})_{0}<10^{-15}m$. Finally, we have shown that the above estimation of minimal length is in good agreement with the results obtained in previous investigations.Comment: 10 pages, no figur

Self-consistent calculation of total energies of the electron gas using many-body perturbation theory

The performance of many-body perturbation theory for calculating ground-state properties is investigated. We present fully numerical results for the electron gas in three and two dimensions in the framework of the GW approximation. The overall agreement with very accurate Monte Carlo data is excellent, even for those ranges of densities for which the GW approach is often supposed to be unsuitable. The latter seems to be due to the fulfillment of general conservation rules. These results open further prospects for accurate calculations of ground-state properties circumventing the limitations of standard density-functional theory

Charged black holes in quadratic gravity

Iterative solutions to fourth-order gravity describing static and electrically charged black holes are constructed. Obtained solutions are parametrized by two integration constants which are related to the electric charge and the exact location of the event horizon. Special emphasis is put on the extremal black holes. It is explicitly demonstrated that in the extremal limit, the exact location of the (degenerate) event horizon is given by \rp = |e|. Similarly to the classical Reissner-Nordstr\"om solution, the near-horizon geometry of the charged black holes in quadratic gravity, when expanded into the whole manifold, is simply that of Bertotti and Robinson. Similar considerations have been carried out for the boundary conditions of second type which employ the electric charge and the mass of the system as seen by a distant observer. The relations between results obtained within the framework of each method are briefly discussed

Krein Regularization of \lambda\phi^4

We calculate the four-point function in \lambda\phi^4 theory by using Krein regularization and compare our result, which is finite, with the usual result in \lambda\phi^4 theory. The effective coupling constant (\lambda_\mu) is also calculated in this method

Regular black holes in quadratic gravity

The first-order correction of the perturbative solution of the coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed, with the zeroth-order solution coinciding with the ones given by Ay\'on-Beato and Garc{\'\i}a and by Bronnikov. It is shown that a simple generalization of the Bronnikov's electromagnetic Lagrangian leads to the solution expressible in terms of the polylogarithm functions. The solution is parametrized by two integration constants and depends on two free parameters. By the boundary conditions the integration constants are related to the charge and total mass of the system as seen by a distant observer, whereas the free parameters are adjusted to make the resultant line element regular at the center. It is argued that various curvature invariants are also regular there that strongly suggests the regularity of the spacetime. Despite the complexity of the problem the obtained solution can be studied analytically. The location of the event horizon of the black hole, its asymptotics and temperature are calculated. Special emphasis is put on the extremal configuration

Tensor calculus for supergravity on a manifold with boundary

Using the simple setting of 3D N=1 supergravity, we show how the tensor calculus of supergravity can be extended to manifolds with boundary. We present an extension of the standard F-density formula which yields supersymmetric bulk-plus-boundary actions. To construct additional separately supersymmetric boundary actions, we decompose bulk supergravity and bulk matter multiplets into co-dimension one submultiplets. As an illustration we obtain the supersymmetric extension of the York-Gibbons-Hawking extrinsic curvature boundary term. We emphasize that our construction does not require any boundary conditions on off-shell fields. This gives a significant improvement over the existing orbifold supergravity tensor calculus.Comment: 20 pages, JHEP format; published versio

Tomographic Representation of Minisuperspace Quantum Cosmology and Noether Symmetries

The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic probability distribution provides the classical evolution for the models and can be considered an approach to select "observable" universes. Some specific examples, derived from Extended Theories of Gravity, are worked out. We discuss also how to connect tomograms, symmetries and cosmological parameters.Comment: 15 page

Reproductive biology of Cattleya eldorado, a species of Orchidaceae from the Amazonian white sand campinas

The orchid plants are highly prized for their lush exotic flowers. It is the largest plant family with more than 24000 species, which indicates a high diversity of forms and adaptations to different environments, including the capacity to attract, deceive and manipulate visitors involved in cross-pollination. Cattleya eldorado occurs in areas of white sand campinas, a typical vegetation type of the Amazon region, which is under strong anthropogenic pressure. This work's main objectives to know the biological processes of C. eldorado providing subsidies to maintain and manage it in its natural habitat. This study was conducted from 2000 to 2006 in the Campina Biological Reserve, during its flowering period. C. eldorado is an epiphytic orchid species that has the melittophyly syndrome and is adapted to its pollinator, the bee Eulaema mocsaryi recognizing their flowers by smell and by visual stimuli, through their color and reflection of ultraviolet light. C. eldorado is self-compatible, even if it requires a pollinating agent for the transfer of the pollinarium until its deposition in the stigmatic cavity of the flower.", 'enAs Orchidaceae são muito apreciadas por suas flores exóticas e exuberantes. É a maior família de plantas apresentando mais de 24000 espécies, o que denota uma alta diversidade de formas e adaptações a diferentes ambientes, como também para atração, engano e manipulação de visitantes na realização da polinização cruzada. Cattleya eldorado ocorre em áreas de campinas, que são formações vegetais típicas da região amazônica, que se encontram sob forte ação antrópica. Este trabalho tem como um de seus principais objetivos conhecer parte dos processos biológicos de C. eldorado fornecendo subsídios para conservá-la e manejá-la em seu habitat natural. Este estudo foi desenvolvido na Reserva Biológica de Campina, de 2000 a 2006, durante a sua floração. C. eldorado é uma espécie epifítica que apresenta a síndrome de melitofilia, estando adaptada ao seu polinizador, a abelha Eulaema mocsaryi, que reconhece suas flores pelo odor e pelo estímulo visual através de sua coloração e reflexão de luz ultravioleta. C. eldorado é uma espécie autocompatível, embora necessite de um agente polinizador para a transferência do polinário até sua deposição na cavidade estigmática da flor