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Francisco S. N. Lobo

Publications and source records attributed to Francisco S. N. Lobo.

At least 307 records · Page 17Linked to original sources
arXiv2007

Conformally symmetric traversable wormholes

Exact solutions of traversable wormholes are found under the assumption of spherical symmetry and the existence of a {\it non-static} conformal symmetry, which presents a more systematic approach in searching for exact wormhole solutions. In this work, a wide variety of solutions are deduced by considering choices for the form function, a specific linear equation of state relating the energy density and the pressure anisotropy, and various phantom wormhole geometries are explored. A large class of solutions impose that the spatial distribution of the exotic matter is restricted to the throat neighborhood, with a cut-off of the stress-energy tensor at a finite junction interface, although asymptotically flat exact solutions are also found. Using the ``volume integral quantifier,'' it is found that the conformally symmetric phantom wormhole geometries may, in principle, be constructed by infinitesimally small amounts of averaged null energy condition violating matter. Considering the tidal acceleration traversability conditions for the phantom wormhole geometry, specific wormhole dimensions and the traversal velocity are also deduced.

gr-qc↗
arXiv2007

Self sustained phantom wormholes in semi-classical gravity

A possible candidate for the late time accelerated expanding Universe is phantom energy, which possesses rather bizarre properties, such as the prediction of a Big Rip singularity and the violation of the null energy condition. The latter is a fundamental ingredient of traversable wormholes, and it has been shown that phantom energy may indeed sustain these exotic geometries. Inspired by the evolving dark energy parameter crossing the phantom divide, we consider in this work a varying equation of state parameter dependent on the radial coordinate, i.e., $ω(r)=p(r)/ρ(r)$. We shall impose that phantom energy is concentrated in the neighborhood of the throat, to ensure the flaring out condition, and several models are analyzed. We shall also consider the possibility that these phantom wormholes be sustained by their own quantum fluctuations. The energy density of the graviton one loop contribution to a classical energy in a phantom wormhole background and the finite one loop energy density are considered as a self-consistent source for these wormhole geometries. The latter semi-classical approach prohibits solutions with a constant equation of state parameter, which further motivates the imposition of a radial dependent parameter, $ω(r)$, and only permits solutions with a steep positive slope proportional to the radial derivative of the equation of state parameter, evaluated at the throat. The size of the wormhole throat as a function of the relevant parameters is also explored.

gr-qc↗
arXiv2007

Stability of the Einstein static universe in f(R) gravity

We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the context of f(R) modified theories of gravity. By considering specific forms of f(R), the stability regions of the solutions are parameterized by a linear equation of state parameter w=p/rho. Contrary to classical general relativity, it is found that in f(R) gravity a stable Einstein cosmos with a positive cosmological constant does indeed exist. Thus, we are lead to conclude that, in principle, modifications in f(R) gravity stabilize solutions which are unstable in general relativity.

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arXiv2007

Extra force in $f(R)$ modified theories of gravity

The equation of motion for test particles in $f(R)$ modified theories of gravity is derived. By considering an explicit coupling between an arbitrary function of the scalar curvature, $R$, and the Lagrangian density of matter, it is shown that an extra force arises. This extra force is orthogonal to the four-velocity and the corresponding acceleration law is obtained in the weak field limit. Connections with MOND and with the Pioneer anomaly are further discussed.

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arXiv2007

A general class of braneworld wormholes

The brane cosmology scenario is based on the idea that our Universe is a 3-brane embedded in a five-dimensional bulk. In this work, a general class of braneworld wormholes is explored with $R\neq 0$, where $R$ is the four dimensional Ricci scalar, and specific solutions are further analyzed. A fundamental ingredient of traversable wormholes is the violation of the null energy condition (NEC). However, it is the effective total stress energy tensor that violates the latter, and in this work, the stress energy tensor confined on the brane, threading the wormhole, is imposed to satisfy the NEC. It is also shown that in addition to the local high-energy bulk effects, nonlocal corrections from the Weyl curvature in the bulk may induce a NEC violating signature on the brane. Thus, braneworld gravity seems to provide a natural scenario for the existence of traversable wormholes.

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arXiv2007

A new two-sphere singularity in general relativity

The Florides solution, proposed as an alternative to the interior Schwarzschild solution, represents a static and spherically symmetric geometry with vanishing radial stresses. It is regular at the center, and is matched to an exterior Schwarzschild solution. The specific case of a constant energy density has been interpreted as the field inside an Einstein cluster. In this work, we are interested in analyzing the geometry throughout the permitted range of the radial coordinate without matching it to the Schwarzschild exterior spacetime at some constant radius hypersurface. We find an interesting picture, namely, the solution represents a three-sphere, whose equatorial two-sphere is singular, in the sense that the curvature invariants and the tangential pressure diverge. As far as we know, such singularities have not been discussed before. In the presence of a large negative cosmological constant (anti-de Sitter) the singularity is removed.

gr-qc↗
arXiv2007

Gravastars supported by nonlinear electrodynamics

Gravastar models have recently been proposed as an alternative to black holes, mainly to avoid the problematic issues associated with event horizons and singularities. In this work, a wide variety of gravastar models within the context of nonlinear electrodynamics are constructed. Using the $F$ representation, specific forms of Lagrangians are considered describing magnetic gravastars, which may be interpreted as self-gravitating magnetic monopoles with charge $g$. Using the dual $P$ formulation of nonlinear electrodynamics, electric gravastar models are constructed by considering specific structural functions, and the characteristics and physical properties of the solutions are further explored. These interior nonlinear electrodynamic geometries are matched to an exterior Schwarzschild spacetime at a junction interface.

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arXiv2007

Van der Waals quintessence stars

The van der Waals quintessence equation of state is an interesting scenario for describing the late universe, and seems to provide a solution to the puzzle of dark energy, without the presence of exotic fluids or modifications of the Friedmann equations. In this work, the construction of inhomogeneous compact spheres supported by a van der Waals equation of state is explored. These relativistic stellar configurations shall be denoted as {\it van der Waals quintessence stars}. Despite of the fact that, in a cosmological context, the van der Waals fluid is considered homogeneous, inhomogeneities may arise through gravitational instabilities. Thus, these solutions may possibly originate from density fluctuations in the cosmological background. Two specific classes of solutions, namely, gravastars and traversable wormholes are analyzed. Exact solutions are found, and their respective characteristics and physical properties are further explored.

gr-qc↗
arXiv2006

Dynamic wormhole spacetimes coupled to nonlinear electrodynamics

We explore the possibility of dynamic wormhole geometries, within the context of nonlinear electrodynamics. The Einstein field equation imposes a contracting wormhole solution and the obedience of the weak energy condition. Furthermore, in the presence of an electric field, the latter presents a singularity at the throat, however, for a pure magnetic field the solution is regular. Thus, taking into account the principle of finiteness, that a satisfactory theory should avoid physical quantities becoming infinite, one may rule out evolving wormhole solutions, in the presence of an electric field, coupled to nonlinear electrodynamics.

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arXiv2006

Stable dark energy stars: An alternative to black holes?

In this work, a generalization of the Mazur-Mottola gravastar model is explored, by considering a matching of an interior solution governed by the dark energy equation of state, $ω\equiv p/ ρ<-1/3$, to an exterior Schwarzschild vacuum solution at a junction interface, situated near to where the event horizon is expected to form. The motivation for implementing this generalization arises from the fact that recent observations have confirmed an accelerated cosmic expansion, for which dark energy is a possible candidate.

gr-qc↗
arXiv2006

Traversable wormholes coupled to nonlinear electrodynamics

In this work we explore the possible existence of static, spherically symmetric and stationary, axisymmetric traversable wormholes coupled to nonlinear electrodynamics. Considering static and spherically symmetric (2+1) and (3+1)-dimensional wormhole spacetimes, we verify the presence of an event horizon and the non-violation of the null energy condition at the throat. For the former spacetime, the principle of finiteness is imposed, in order to obtain regular physical fields at the throat. Next, we analyze the (2+1)-dimensional stationary and axisymmetric wormhole, and also verify the presence of an event horizon, rendering the geometry non-traversable. Relatively to the (3+1)-dimensional stationary and axisymmetric wormhole geometry, we find that the field equations impose specific conditions that are incompatible with the properties of wormholes. Thus, we prove the non-existence of the general class of traversable wormhole solutions, outlined above, within the context of nonlinear electrodynamics.

gr-qc↗
arXiv2006

Evolving wormhole geometries within nonlinear electrodynamics

In this work, we explore the possibility of evolving (2+1) and (3+1)-dimensional wormhole spacetimes, conformally related to the respective static geometries, within the context of nonlinear electrodynamics. For the (3+1)-dimensional spacetime, it is found that the Einstein field equation imposes a contracting wormhole solution and the obedience of the weak energy condition. Nevertheless, in the presence of an electric field, the latter presents a singularity at the throat, however, for a pure magnetic field the solution is regular. For the (2+1)-dimensional case, it is also found that the physical fields are singular at the throat. Thus, taking into account the principle of finiteness, which states that a satisfactory theory should avoid physical quantities becoming infinite, one may rule out evolving (3+1)-dimensional wormhole solutions, in the presence of an electric field, and the (2+1)-dimensional case coupled to nonlinear electrodynamics.

gr-qc↗
arXiv2006

Stable phantom energy traversable wormhole models

A possible candidate for the present accelerated expansion of the Universe is ''phantom energy'', which possesses an equation of state of the form $ω\equiv p/ρ<-1$, consequently violating the null energy condition. As this is the fundamental ingredient to sustain traversable wormholes, this cosmic fluid presents us with a natural scenario for the existence of these exotic geometries. In this context, we shall construct phantom wormhole geometries by matching an interior wormhole solution, governed by the phantom energy equation of state, to an exterior vacuum at a junction interface. Several physical properties and characteristics of these solutions are further investigated. The dynamical stability of the transition layer of these phantom wormholes to linearized spherically symmetric radial perturbations about static equilibrium solutions is also explored. It is found that the respective stable equilibrium configurations may be increased by strategically varying the wormhole throat radius.

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arXiv2006

Chaplygin traversable wormholes

The generalized Chaplygin gas (GCG) is a candidate for the unification of dark energy and dark matter, and is parametrized by an exotic equation of state given by $p_{ch}=-A/ρ_{ch}^α$, where $A$ is a positive constant and $0<α\leq 1$. In this paper, exact solutions of spherically symmetric traversable wormholes supported by the GCG are found, possibly arising from a density fluctuation in the GCG cosmological background. To be a solution of a wormhole, the GCG equation of state imposes the following generic restriction $A<(8πr_0^2)^{-(1+α)}$, where $r_0$ is the wormhole throat radius, consequently violating the null energy condition. The spatial distribution of the exotic GCG is restricted to the throat neighborhood, and the physical properties and characteristics of these Chaplygin wormholes are further analyzed. Four specific solutions are explored in some detail, namely, that of a constant redshift function, a specific choice for the form function, a constant energy density, and finally, isotropic pressure Chaplygin wormhole geometries.

gr-qc↗
arXiv2006

Stable dark energy stars

The gravastar picture is an alternative model to the concept of a black hole, where there is an effective phase transition at or near where the event horizon is expected to form, and the interior is replaced by a de Sitter condensate. In this work, a generalization of the gravastar picture is explored, by considering a matching of an interior solution governed by the dark energy equation of state, $ω\equiv p/ ρ<-1/3$, to an exterior Schwarzschild vacuum solution at a junction interface. The motivation for implementing this generalization arises from the fact that recent observations have confirmed an accelerated cosmic expansion, for which dark energy is a possible candidate. Several relativistic dark energy stellar configurations are analyzed by imposing specific choices for the mass function. The first case considered is that of a constant energy density, and the second choice, that of a monotonic decreasing energy density in the star's interior. The dynamical stability of the transition layer of these dark energy stars to linearized spherically symmetric radial perturbations about static equilibrium solutions is also explored. It is found that large stability regions exist that are sufficiently close to where the event horizon is expected to form, so that it would be difficult to distinguish the exterior geometry of the dark energy stars, analyzed in this work, from an astrophysical black hole.

gr-qc↗
arXiv2005

Stability analysis of dynamic thin shells

We analyze the stability of generic spherically symmetric thin shells to linearized perturbations around static solutions. We include the momentum flux term in the conservation identity, deduced from the ''ADM'' constraint and the Lanczos equations. Following the Ishak-Lake analysis, we deduce a master equation which dictates the stable equilibrium configurations. Considering the transparency condition, we study the stability of thin shells around black holes, showing that our analysis is in agreement with previous results. Applying the analysis to traversable wormhole geometries, by considering specific choices for the form function, we deduce stability regions, and find that the latter may be significantly increased by considering appropriate choices for the redshift function.

gr-qc↗
arXiv2005

Stability of phantom wormholes

It has recently been shown that traversable wormholes may be supported by phantom energy. In this work phantom wormhole geometries are modelled by matching an interior traversable wormhole solution, governed by the equation of state $p=ωρ$ with $ω<-1$, to an exterior vacuum spacetime at a finite junction interface. The stability analysis of these phantom wormholes to linearized spherically symmetric perturbations about static equilibrium solutions is carried out. A master equation dictating the stability regions is deduced, and by separating the cases of a positive and a negative surface energy density, it is found that the respective stable equilibrium configurations may be increased by strategically varying the wormhole throat radius. The first model considered, in the absence of a thin shell, is that of an asymptotically flat phantom wormhole spacetime. The second model constructed is that of an isotropic pressure phantom wormhole, which is of particular interest, as the notion of phantom energy is that of a spatially homogeneous cosmic fluid, although it may be extended to inhomogeneous spherically symmetric spacetimes.

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