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In this work we explore a Holographic Dark Energy Model in a flat Friedmann-Lemaître-Robertson-Walker Universe, which contains baryons, radiation, cold dark matter and dark energy within the framework of General Relativity. Furthermore, we consider three types of phenomenological interactions in the dark sector. With the proposed model we obtained the algebraic expressions for the cosmological parameters of our interest: the deceleration and coincidence parameters. Likewise, we graphically compare the proposed model with the ACDM model. Resumen En este trabajo exploramos un modelo de energía oscura holográfica en un universo plano de Friedmann-Lemaître-Robertson-Walker, que contiene bariones, radiación, materia oscura fría y energía oscura en el marco de la relatividad general. Además, consideramos tres tipos de interacciones fenomenológicas en el sector oscuro. Con el modelo propuesto obtuvimos las expresiones algebraicas para los parámetros cosmológicos de nuestro interés: los parámetros de desaceleración y coincidencia. Del mismo modo, comparamos gráficamente el modelo propuesto con el modelo ACDM.

In this work we study the thermodynamics of a ($2+1$)-dimensional static black hole under a nonlinear electric field. In addition to standard approaches, we investigate black hole thermodynamic geometry. We compute Weinhold and Ruppeiner metrics and compare the thermodynamic geometries with the standard description for black hole thermodynamics. We further consider the cosmological constant as an additional extensive thermodynamic variable. For thermodynamic equilibrium in three-dimensional space, we compute heat engine efficiency and show that it may be constructed with this black hole.

We perform a Bayesian model selection analysis for interacting scenarios of dark matter and modified holographic Ricci dark energy (MHRDE) with linear interacting terms. We use a combination of some of the latest cosmological data such as type Ia supernovae, cosmic chronometers, cosmic microwave background and baryon acoustic oscillations measurements. We find strong evidence against all the MHRDE interacting scenarios studied with respect to $\Lambda$CDM when the full joint analysis is considered., Comment: 13 pages, 4 figures

In this paper we derive new static phantom traversable wormholes by assuming a shape function with a quadratic dependence on the radial coordinate r. We mainly focus our study on wormholes sustained by exotic matter with positive energy density (as seen by any static observer) and a variable equation of state $p_r/\rho, Comment: To be published in Physical Review D; 9 pages; 8 figures

We provide a detailed description for power--law scaling Friedmann-Robertson-Walker cosmological scenarios dominated by two interacting perfect fluid components during the expansion. As a consequence of the mutual interaction between the two fluids, neither component is conserved separately and the energy densities are proportional to $1/t^{2}$. It is shown that in flat FRW cosmological models there can exist interacting superpositions of two perfect fluids (each of them having a positive energy density) which accelerate the expansion of the universe. In this family there also exist flat power law cosmological scenarios where one of the fluids may have a ``cosmological constant" or "vacuum energy" equation of state ($p =-\rho$) interacting with the other component; this scenario exactly mimics the behavior of the standard flat Friedmann solution for a single fluid with a barotropic equation of state. These possibilities of combining interacting perfect fluids do not exist for the non-interacting mixtures of two perfect cosmic fluids, where the general solution for the scale factor is not described by power--law expressions and has a more complicated behavior. In this study is considered also the associated single fluid model interpretation for the interaction between two fluids., Comment: 10 pages. Accepted for publication in Physics Letters B

In order to investigate if the anisotropy of the spacetime may induce future singularities at a finite value of the cosmic time on the evolution of cosmological models, we study vacuum and non-vacuum Bianchi type I spacetimes exhibiting such future singularities. We show that in the case of Kasner vacuum cosmologies the spacetime may rip itself apart in a finite time, and only in the direction corresponding to the unique scale factor which diverges at this finite value of the cosmic time. The other two directional scale factors and the average scale factor do not diverge and tend to zero at this time, while the directional and average expansion rates also become infinite. Due to the absence of the matter content this anisotropic future singularity is induced by the shear scalar, which also blows up at this time. We call such a singularity "Vacuum Rip". For non-vacuum solutions we discuss fully anisotropic Bianchi type I spacetimes filled with a stiff fluid and ellipsoidal (axisymmetric) cosmological models filled with matter with isotropic and anisotropic barotropic pressure, and characterized by $\sigma/\theta=const$, where $\sigma$ and $\theta$ are the shear scalar and the expansion scalar respectively., Comment: 10 pages, 6 figures, Accepted for publication in Journal of Mathematical Physics (2016)

In order to study if the bulk viscosity may induce a big rip singularity on the flat FRW cosmologies, we investigate dissipative processes in the universe within the framework of the standard Eckart theory of relativistic irreversible thermodynamics, and in the full causal Israel–Stewart–Hiscock theory. We have found cosmological solutions which exhibit, under certain constraints, a big rip singularity. We show that the negative pressure generated by the bulk viscosity cannot avoid that the dark energy of the universe to be phantom energy.

We study a closed model of the universe filled with viscous fluid and quintessence matter components in a Brans-Dicke type cosmological model. The dynamical equations imply that the universe may look like an accelerated flat Friedmann-Robertson-Walker universe at low redshift. We consider here dissipative processes which follow a causal thermodynamics. The theory is applied to viscous fluid inflation, where accepted values for the total entropy in the observable universe is obtained., 11 pages, revtex 4. For a festschrift honoring Alberto Garcia. To be publishen in Gen. Rel. Grav

We study a closed model of a universe filled with viscous fluid and quintessence matter components. The dynamical equations imply that the universe might look like an accelerated flat Friedmann-Robertson-Walker (FRW) universe at low redshift. We consider here dissipative processes which obey a causal thermodynamics. Here, we account for the entropy production via causal dissipative inflation., 9 pages. Accepted for publication in IJMPD

The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic field: two for the vector electric field and one for the scalar magnetic field. It is shown that we can not have any superposition of these components of the electric and magnetic fields in this kind of static gravitational field. One of the electrostatic Einstein-Maxwell solutions is related to the magnetostatic solution by a duality mapping, while the second electrostatic gravitational field must be solved separately. Solutions induced by the more general (2+1)-Maxwell tensor on the static cylindrically symmetric spacetimes are studied and it is shown that all of them are also connected by duality mappings., Comment: 5 pages, Final version

La presente investigacion se realizo con la finalidad de cuantificar los efectos del enriquecimiento polisensorial temprano sobre el desarrollo de celulas piramidales de la corteza parietal, en ratas que simultaneamente fueron sometidas a desnutricion calorico-proteica. Un breve periodo de estimulacion durante el periodo de lactancia disminuyo significativamente la densidad celular en la placa cortical (indice evolutivo filogenetico-ontogenetico). Los resultados sugieren que la corteza cerebral se desarrolla de acuerdo con una red neuronal altamente sofisticada, la cual exhibe un notable grado de especificidad estructural regulada por claves geneticas y ambientales. La prediccion mas obvia es que las influencias ambientales son probablemente traducidas como expresion estructural en la placa cortical parietal.

We consider a five-dimensional Einstein-Chern-Simons action which is composed of a gravitational sector and a sector of matter, where the gravitational sector is given by a Chern-Simons gravity action instead of the Einstein-Hilbert action and where the matter sector is given by the so called perfect fluid. It is shown that (i) the Einstein-Chern-Simons (EChS) field equations subject to suitable conditions can be written in a similar way to the Einstein-Maxwell field equations; (ii) these equations have solutions that describe accelerated expansion for the three possible cosmological models of the universe, namely, spherical expansion, flat expansion and hyperbolic expansion when $\alpha $, a parameter of theory, is greater than zero. This result allow us to conjeture that this solutions are compatible with the era of Dark Energy and that the energy-momentum tensor for the field $h^{a}$, a bosonic gauge field from the Chern-Simons gravity action, corresponds to a form of positive cosmological constant. It is also shown that the EChS field equations have solutions compatible with the era of matter: (i) In the case of an open universe, the solutions correspond to an accelerated expansion ($\alpha >0$) with a minimum scale factor at initial time that, when the time goes to infinity, the scale factor behaves as a hyperbolic sine function. (ii) In the case of a flat universe, the solutions describing an accelerated expansion whose scale factor behaves as a exponencial function when time grows. \item In the case of a closed universe it is found only one solution for a universe in expansion, which behaves as a hyperbolic cosine function when time grows., Comment: 58 pages, 24 figures

We propose an approach for constructing spatial slices of (3+1) spacetimes with cosmological constant but without a matter content, which yields (2+1) vacuum with Λ solutions. The reduction mechanism from (3+1) to (2+1) gravity is supported on a criterion in which the Weyl tensor components are required to vanish together with a dimensional reduction via an appropriate foliation. By using an adequate reduction mechanism from the Plebanski–Carter[A] solution in (3+1) gravity, the (2+1) BTZ solution can be obtained.

The most general charged version of the spinning BTZ black hole solution assuming an (anti-) self dual condition imposed on the orthonormal basis components of the electric and magnetic fields is obtained. It is found that the one-parameter Kamata-Koikawa field is a particular solution of our general solution. A spinning magnetic solution is also found. It is shown that a duality mapping exists among spinning solutions obtained from electrostatic and magnetostatic fields with the help of the local transformation t→t−ωθ, θ→θ−ωt .

We reconsider the cosmological model discussed by Sung-Won Kim [Phys. Rev D 53, 6889 (1996)] in the context of Friedmann-Robertson-Walker cosmologies with a traversable wormhole, where it is assumed that the matter content is divided into two parts: the cosmic part that depends on time only and the wormhole part that depends on space only. The cosmic part obeys the barotropic equation of state $p_c=\gamma \rho_c$. The complete analysis requires further care and reveals more interesting results than what was previously shown by the author. They can be readily applied to the evolution of a large class of cosmological models which are more general than FRW models., Comment: 4 pages, To be published in Physical Review D

We investigate a family of inhomogeneous and anisotropic gravitational fields exhibiting a future singularity at a finite value of the proper time. The studied spherically symmetric spacetimes are asymptotically Friedmann-Robertson-Walker at spatial infinity and describe wormhole configurations filled with two matter components: one inhomogeneous and anisotropic fluid and another isotropic and homogeneously distributed fluid, characterized by the supernegative equation of state \omega=p/\rho < -1. In previously constructed wormholes, the notion of the phantom energy was used in a more extended sense than in cosmology, where the phantom energy is considered a homogeneously distributed fluid. Specifically, for some static wormhole geometries the phantom matter was considered as an inhomogeneous and anisotropic fluid, with radial and lateral pressures satisfying the relations $p_{r}/\rho, Comment: 9 pages, 9 figures, accepted for publication in Phys. Rev. D

In this article we investigate and develop specific aspects of Friedmann-Robertson-Walker (FRW) scalar field cosmologies related to the interpretation that canonical and phantom scalar field sources may be interpreted as cosmological configurations with a mixture of two interacting barotropic perfect fluids: a matter component $\rho_1(t)$ with a stiff equation of state ($p_1=\rho_1$), and an "effective vacuum energy" $\rho_2(t)$ with a cosmological constant equation of state ($p_2=-\rho_2$). An important characteristic of this alternative equivalent formulation in the framework of interacting cosmologies is that it gives, by choosing a suitable form of the interacting term $Q$, an approach for obtaining exact and numerical solutions. The choice of $Q$ merely determines a specific scalar field with its potential, thus allowing to generate closed, open and flat FRW scalar field cosmologies., Comment: 9 pages, accepted for publication in Astrophys Space Sci

In this paper we study $(N+1)$-dimensional evolving wormholes supported by energy satisfying a polytropic equation of state. The considered evolving wormhole models are described by a constant redshift function and generalizes the standard flat Friedmann-Robertson-Walker spacetime. The polytropic equation of state allows us to consider in $(3+1)$-dimensions generalizations of the phantom energy and the generalized Chaplygin gas sources., Comment: 6 pages, 2 figures, accepted for publication in European Physical Journal C

We develop a model for the gravitational field which is renormalizable, conformally invariant and integrable in four dimensions. The first two conditions can be easily implemented. However, for the latter condition we must take recourse to fourth-rank geometry where the line element is defined by a quartic form, . The simplest Lagrangian which can be constructed in this case depends quadratically on a Ricci tensor constructed only in terms of a connection; therefore a Palatini-like variational principle is applied. The field equations imply that the fourth-rank metric decomposes into a product of a second-rank metric with itself, and in this case the geometry becomes Riemannian. The decomposition of the fourth-rank metric means our field equations become linear in the Ricci tensor and thus they are amenable for comparison with the Einstein field equations. We show that the Einstein field equations are a particular case of our field equations. The field equations are solved in the spherically symmetric case. The solution contains the Schwarzschild metric and the Kottler metric, corresponding to a massive point particle on a Minkowski and a de Sitter background, respectively.

We obtain the Einstein-Maxwell equations for (2+1)-dimensional static space-time, which are invariant under the transformation $q_0=i\,q_2,q_2=i\,q_0,\alpha \rightleftharpoons \gamma$. It is shown that the magnetic solution obtained with the help of the procedure used in Ref.~\cite{Cataldo}, can be obtained from the static BTZ solution using an appropriate transformation. Superpositions of a perfect fluid and an electric or a magnetic field are separately studied and their corresponding solutions found., Comment: 8 pages, LaTeX, no figures, to appear in Physical Review D

We investigate the evolution of a family of wormholes sustained by two matter components: one with homogeneous and isotropic properties $\rho(t)$ and another inhomogeneous and anisotropic $\rho_{in}(t,r)$. The rate of expansion of these evolving wormholes is only determined by the isotropic and homogeneous matter component $\rho(t)$. Particularly, we consider a family of exact two-fluid evolving wormholes expanding with constant velocity and satisfying the dominant and the strong energy conditions in the whole spacetime. In general, for the case of vanishing isotropic fluid $\rho(t)$ and cosmological constant $\Lambda$ the space expands with constant velocity, and for $\rho(t)=0$ and $\Lambda \neq 0$ the rate of expansion is determined by the cosmological constant. The considered here two-fluid evolving wormholes are a generalization of single fluid models discussed in previous works of the present authors [Phys.\ Rev.\ D {\bf 78}, 104006 (2008); Phys.\ Rev.\ D {\bf 79}, 024005 (2009)]., Comment: 8 pages, to be published in Phys. Rev D

On the basis of the approach to generation of Einstein-Maxwell fields proposed by Jan Horský and Nikolai Mitskievich, a magnetization of the pencil-of-light space-time is performed yielding a superposition of the fields of a spinning pencil of light and of the Bonnor-Melvin universe. An interplay of Petrov's types in this superposition is revealed. A generalization of Wald's theorem on test electromagnetic fields on a vacuum space-time background is achieved thus explaining applicability of our approach to space-times of the Levi-Civita type.

It is well known that Kasner-type cosmologies provide a useful framework for analyzing the three-dimensional anisotropic expansion because of the simplification of the anisotropic dynamics. In this paper relativistic multi-fluid Kasner-type scenarios are studied. We first consider the general case of a superposition of two ideal cosmic fluids, as well as the particular cases of non-interacting and interacting ones, by introducing a phenomenological coupling function $q(t)$. For two-fluid cosmological scenarios there exist only cosmological scaling solutions, while for three-fluid configurations there exist not only cosmological scaling ones, but also more general solutions. In the case of triply interacting cosmic fluids we can have energy transfer from two fluids to a third one, or energy transfer from one cosmic fluid to the other two. It is shown that by requiring the positivity of energy densities there always is a matter component which violates the dominant energy condition in this kind of anisotropic cosmological scenarios., Accepted for publication in Astrophysics &Space Science, 8 pages

In this paper we consider a spatially flat Friedmann-Robertson-Walker (FRW) cosmological model with cosmological constant, containing a stiff fluid and a classical Dirac field. The proposed cosmological scenario describes the evolution of effective dark matter and dark energy components reproducing, with the help of that effective multifluid configuration, the quintessential behavior. We find the value of the scale factor where the effective dark energy component crosses the phantom divide. The model we introduce, which can be considered as a modified $\Lambda$CDM one, is characterized by a set of parameters which may be constrained by the astrophysical observations available up to date., Comment: Accepted for publication in Astrophysics & Space Science, 10 pages, 6 figures

We present a family of static and evolving spherically symmetric Lorentzian wormhole solutions in N+1 dimensional Einstein gravity. In general, for static wormholes, we require that at least the radial pressure has a barotropic equation of state of the form $p_r=\omega_r \rho$, where the state parameter $\omega_r$ is constant. On the other hand, it is shown that in any dimension $N \geq 3$, with $\phi(r)=\Lambda=0$ and anisotropic barotropic pressure with constant state parameters, static wormhole configurations are always asymptotically flat spacetimes, while in 2+1 gravity there are not only asymptotically flat static wormholes and also more general ones. In this case, the matter sustaining the three-dimensional wormhole may be only a pressureless fluid. In the case of evolving wormholes with $N \geq 3$, the presence of a cosmological constant leads to an expansion or contraction of the wormhole configurations: for positive cosmological constant we have wormholes which expand forever and, for negative cosmological constant we have wormholes which expand to a maximum value and then recollapse. In the absence of a cosmological constant the wormhole expands with constant velocity, i.e without acceleration or deceleration. In 2+1 dimensions the expanding wormholes always have an isotropic and homogeneous pressure, depending only on the time coordinate., Comment: 10 pages, accepted for publication in Phys. Rev. D

We study Friedmann-Robertson-Walker cosmological models with matter content composed of two perfect fluids $\rho_1$ and $\rho_2$, with barotropic pressure densities $p_1/ \rho_1=\omega_1=const$ and $p_2/ \rho_2=\omega_2=const$, where one of the energy densities is given by $\rho_1=C_1 a^\alpha + C_2 a^\beta$, with $C_1$, $C_2$, $\alpha$ and $\beta$ taking constant values. We solve the field equations by using the conservation equation without breaking it into two interacting parts with the help of a coupling interacting term $Q$. Nevertheless, with the found solution may be associated an interacting term $Q$, and then a number of cosmological interacting models studied in the literature correspond to particular cases of our cosmological model. Specifically those models having constant coupling parameters $\tilde{\alpha}$, $\tilde{\beta}$ and interacting terms given by $Q=\tilde{\alpha} H \rho_{_{DM}}$, $Q=\tilde{\alpha} H \rho_{_{DE}}$, $Q=\tilde{\alpha} H (\rho_{_{DM}}+ \rho_{_{DE}})$ and $Q=\tilde{\alpha} H \rho_{_{DM}}+\tilde{\beta} H \rho_{_{DE}}$, where $\rho_{_{DM}}$ and $\rho_{_{DE}}$ are the energy densities of dark matter and dark energy respectively. The studied set of solutions contains a class of cosmological models presenting a scaling behavior at early and at late times. On the other hand the two-fluid cosmological models considered in this paper also permit a three fluid interpretation which is also discussed. In this reinterpretation, for flat Friedmann-Robertson-Walker cosmologies, the requirement of positivity of energy densities of the dark matter and dark energy components allows the state parameter of dark energy to be in the range $-1.37 \lesssim \omega_{_{DE}}, Comment: 17 pages, 10 figures

In this paper we study the possibility of sustaining an evolving wormhole via exotic matter made of phantom energy in the presence of a cosmological constant. We derive analytical evolving wormhole geometries by supposing that the radial tension of the phantom matter, which is negative to the radial pressure, and the pressure measured in the tangential directions have barotropic equations of state with constant state parameters. In this case the presence of a cosmological constant ensures accelerated expansion of the wormhole configurations. More specifically, for positive cosmological constant we have wormholes which expand forever and, for negative cosmological constant we have wormholes which expand to a maximum value and then recolapse. At spatial infinity the energy density and the pressures of the anisotropic phantom matter threading the wormholes vanish; thus these evolving wormholes are asymptotically vacuum $\Lambda$-Friedmann models with either open or closed or flat topologies., Comment: 8 pages. To appear in Physical Review D

In this paper we study the possibility of sustaining an evolving wormhole via exotic matter made out of phantom energy. We show that this exotic source can support the existence of evolving wormhole spacetimes. Explicitly, a family of evolving Lorentzian wormholes conformally related to another family of zero-tidal force static wormhole geometries is found in Einstein gravity. Contrary to the standard wormhole approach, where first a convenient geometry is fixed and then the matter distribution is derived, we follow the conventional approach for finding solutions in theoretical cosmology. We derive an analytical evolving wormhole geometry by supposing that the radial tension (which is negative to the radial pressure) and the pressure measured in the tangential directions have barotropic equations of state with constant state parameters. At spatial infinity this evolving wormhole, supported by this anisotropic matter, is asymptotically flat, and its slices $t=$ constant are spaces of constant curvature. During its evolution the shape of the wormhole expands with constant velocity, i.e without acceleration or deceleration, since the scale factor has strictly a linear evolution., 9 pages, 2 figures, Accepted for publication in Phys. Rev. D

Previously it was shown that there exists a class of viscous cosmological models which violate the dominant energy condition for a limited amount of time after which they are smoothly connected to the ordinary radiation era (which preserves the dominant energy conditions). This violation of the dominant energy condition at an early cosmological epoch may influence the slopes of energy spectra of relic gravitons that might be of experimental relevance. However, the bulk viscosity coefficient of these cosmologies became negative during the ordinary radiation era, and then the entropy of the sources driving the geometry decreases with time. We show that in the presence of viscous sources with a linear barotropic equation of state $p=\gamma \rho$ we get viscous cosmological models with positive bulk viscous stress during all their evolution, and hence the matter entropy increases with the expansion time. In other words, in the framework of viscous cosmologies, there exist isotropic models compatible with the standard second law of thermodynamics which also may influence the slopes of energy spectra of relic gravitons., Comment: 5 pages, 4 figures

Circularly symmetric charged perfect-fluid distributions are studied in three-dimensional gravity with a cosmological constant. We derive the Tolman-Oppenheimer-Volkoff equation of hydroelectrostatic equilibrium, and we discuss its applicability. A class of charged fluid distributions for $p=\ensuremath{-}\ensuremath{\rho}$ is considered. In this case, a particular model is obtained which represents a charged distribution whose mass is entirely of electromagnetic origin.

In the framework of the n‐dimensional Friedmann‐Robertson‐Walker cosmology, defined for a single scalar field minimally coupled to gravity in the presence of a perfect fluid, the n‐dimensional spatially flat Lucchin‐Mataresse, Barrow‐Burd‐Landcaster‐Madsen, and Barrow‐Saich cosmological solutions are determined.

We study a model in which a closed universe with dust and quintessence matter components may look like an accelerated flat Friedmann-Robertson-Walker (FRW) universe at low redshifts. Several quantities relevant to the model are expressed in terms of observed density parameters, $\Omega_M$ and $\Omega_{\Lambda}$, and of the associated density parameter $\Omega_Q$ related to the quintessence scalar field $Q$., Comment: 11 pages. For a festschrift honoring Alberto Garcia. To appear in Gen. Rel. Grav

We illustrate how the group of symmetry transformations, which preserve the form of the n--dimensional flat Friedmann--Robertson--Walker cosmologies satisfying Einstein equations, acts in any dimension. This group relates the energy density and the isotropic pressure of the cosmic fluid to the expansion rate. The freedom associated with the dimension of the space time yields assisted inflation even when the energy density of the fluid is a dimensional invariant and enriches the set of duality transformations leading to phantom cosmologies., Comment: Accepted for publication in Iternational Journal of Modern Physics D

It is shown that Friedmann–Robertson–Walker (FRW) cosmological models coupled to a single scalar field and to a perfect fluid fitting a wide class of matter perfect fluid state equations, determined in (3+1) dimensional gravity can be related to their (2+1) cosmological counterparts, and vice-versa, by using simple algebraic rules relating gravitational constants, state parameters, perfect fluid and scalar field characteristics. It should be pointed out that the demonstration of these relations for the scalar fields and potentials does not require the fulfilment of any state equation for the scalar field energy density and pressure. As far as to the perfect fluid is concerned, one has to demand the fulfilment of state equations of the form p+ρ = γ f(ρ). If the considered cosmologies contain the inflation field alone, then any (3+1) scalar field cosmology possesses a (2+1) counterpart, and vice-versa. Various families of solutions are derived, and we exhibited their correspondence; for instance, solutions for pure matter perfect fluids and single scalar field fulfilling linear state equations, solutions for scalar fields coupled to matter perfect fluids, a general class of solutions for scalar fields subjected to a state equation of the form p φ+ρφ = γρφ β are reported, in particular Barrow–Saich, and Barrow–Burd–Lancaster–Madsen solutions are exhibited explicitly, and finally perfect fluid solutions for polytropic state equations are given.

The three--dimensional magnetic solution to the Einstein--Maxwell field equations have been considered by some authors. Several interpretations have been formulated for this magnetic spacetime. Up to now this solution has been considered as a two--parameter self--consistent field. We point out that the parameter related to the mass of this solution is just a pure gauge and can be rescaled to minus one. This implies that the magnetic metric has really a simple form and it is effectively one-parameter solution, which describes a distribution of a radial magnetic field in a 2+1 anti--de Sitter background space--time. We consider an alternative interpretation to the Dias--Lemos one for the magnetic field source., 3 pages, accepted for publication

It is shown that, from any n-dimensional Friedmann-Robertson-Walker (FRW) cosmology determined for a single scalar field minimally coupled to gravity, one can construct its m-dimensional counterpart, under the assumption of a common time coordinate and a structurally invariant scale factor for both spacetimes, by means of a simple algebraic correspondence relating gravitational constants and scalar field structural functions. If the considered cosmologies are supplemented with a perfect fluid, fitting a wide class of state equations of the form $p+\ensuremath{\rho}=\ensuremath{\gamma}f(\ensuremath{\rho}),$ then any n-dimensional FRW cosmology, coupled to a perfect fluid and a scalar field, possesses an m-dimensional counterpart, and vice versa. In particular, these assertions hold for single scalar field inflation models. A theorem on this respect is demonstrated. Various families of solutions are explicitly given and exhibit their correspondence with 3+1 cosmological spacetimes.

In this work we establish the correspondence between solutions to the Friedmann-Robertson-Walker cosmologies for perfect fluid and scalar field sources, where both satisfy state equations of the form $p+\ensuremath{\rho}=\ensuremath{\gamma}f(\ensuremath{\rho}),$ not necessarily linear ones. Such state equations are of common use in the case of matter fluids; nevertheless, for a scalar field, they introduce relationships on the potential and kinetic scalar field energies which restrict the set of solutions. A theorem in this respect is demonstrated: From any given $3+1$ cosmological solution, obeying the quoted state equations, one can derive its $2+1$ cosmological counterpart or vice versa. Some applications are given.

It is shown that the supersymmetric extension of the Stelle-West formalism permits the construction of an action for $(3+1)$-dimensional $N=1$ supergravity with a cosmological constant genuinely invariant under the $\mathrm{OSp}(4/1).$ Since the action is invariant under the supersymmetric extension of the AdS group, the supersymmetry algebra closes off shell without the need for auxiliary fields. The limit case $\stackrel{\ensuremath{\rightarrow}}{m}0,$ i.e., $(3+1)$-dimensional $N=1$ supergravity, invariant under the Poincar\'e supergroup is also discussed.

It is shown that the Stelle-West Grignani-Nardelli-formalism allows, both when odd dimensions and when even dimensions are considered, constructing actions for higher dimensional gravity invariant under local Lorentz rotations and under local Poincar\`{e} translations. It is also proved that such actions have the same coefficients as those obtained by Troncoso and Zanelli in ref. Class. Quantum Grav. 17 (2000) 4451., Comment: 7 pages, Latex, accepted in Phys. Rev. D

A family of spherically symmetric, static and self--dual Lorentzian wormholes is obtained in n--dimensional Einstein gravity. This class of solutions includes the n--dimensional versions of the Schwarzschild black hole and the spatial--Schwarzschild traversable wormhole. Using isotropic coordinates we study the geometrical structure of the solution, and delineate the domains of the free parameters for which wormhole, naked singular geometries and the Schwarzschild black hole are obtained. It is shown that, in the lower dimensional Einstein gravity without cosmological constant, we can not have self--dual Lorentzian wormholes., Comment: 6 pages, Latex, accepted in Phys. Rev. D

An action for 3+1-dimensional supergravity genuinely invariant under the Poincare supergroup is proposed. The construction of the action is carried out considering a bosonic lagrangian invariant under both local Lorentz rotations and local Poincare translations as well as under diffeomorphism, and therefore the Poincare algebra closes off-shell. Since the lagrangian is invariant under the Poincare supergroup, the supersymmetry algebra closes off shell without the need of auxiliary fields., Comment: 6 pages, Latex