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J. Ponce de Leon

Publications and source records attributed to J. Ponce de Leon.

At least 19 recordsLinked to original sources
arXiv2017

Regular Reissner-Nordström black hole solutions from linear electrodynamics

In recent years there have appeared in the literature a large number of static, spherically symmetric metrics, which are regular at the origin, asymptotically flat, and have both an event and a Cauchy horizon for certain range of the parameters. They have been interpreted as regular black hole (BH) spacetimes, and their physical source attributed to electric or magnetic monopoles in a suitable chosen nonlinear electrodynamics. Here we show that these metrics can also be interpreted as exact solutions of the Einstein equations coupled to ordinary linear electromagnetism{\textemdash}i.e., as sources of the Reissner-Nordström (RN) spacetime{\textemdash}provided the components of the effective energy-momentum tensor satisfy the dominant energy condition (DEC). We use some well-known regular BH metrics to construct nonsingular RN black holes, where the singularity at the RN center is replaced by a regular perfect fluid charged sphere (whose charge-to-mass ratio is not greater than $1$) which is inside the RN inner horizon.

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arXiv2015

Embeddings for General Relativity

We present a systematic approach to embed $n$-dimensional vacuum general relativity in an $(n + 1)$-dimensional pseudo-Riemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimally-coupled to Einstein gravity. Our approach allows us to generalize a number of results discussed in the literature. We construct {\it all} the possible (physically distinct) embeddings in Einstein spaces, including the Ricci-flat ones widely discussed in the literature. We examine in detail their generalization, which - in the framework under consideration - are higher-dimensional spacetimes sourced by a scalar field with flat (constant $\neq 0$) potential. We use the Kretschmann curvature scalar to show that many embedding spaces have a physical singularity at some finite value of the extra coordinate. We develop several classes of embeddings that are free of singularities, have distinct non-vanishing self-interacting potentials and are continuously connected (in various limits) to Einstein embeddings. We point out that the induced metric possesses scaling symmetry and, as a consequence, the effective physical parameters (e.g., mass, angular momentum, cosmological constant) can be interpreted as functions of the extra coordinate.

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arXiv2012

Cosmological model with variable equations of state for matter and dark energy

We construct a cosmological model which is physically reasonable, mathematically tractable, and extends the study of CDM models to the case where the equations of state (EoS) for matter and dark energy (DE) vary with time. It is based on the assumptions of (i) flatness, (ii) validity of general relativity, (iii) the presence of a DE component that varies between two asymptotic values, (iv) the matter of the universe smoothly evolves from an initial radiation stage - or a barotropic perfect fluid - to a phase where it behaves as cosmological dust at late times. The model approximates the CDM ones for small $z$ but significantly differ from them for large $z$. We focus our attention on how the evolving EoS for matter and DE can modify the CDM paradigm. We discuss a number of physical scenarios. One of them includes, as a particular case, the so-called generalized Chaplygin gas models where DE evolves from non-relativistic dust. Another kind of models shows that the current accelerated expansion is compatible with a DE that behaves like pressureless dust at late times. We also find that a universe with variable DE can go from decelerated to accelerated expansion, and vice versa, several times.

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arXiv2010

Schwarzschild-like exteriors for stars in Kaluza-Klein gravity

In this work we examine the effective four-dimensional world that emanates from a general class of static spherical Ricci-flat solutions in Kaluza-Klein gravity in $D$-dimensions. By means of dimensional reduction we obtain a family of asymptotically flat Schwarzschild-like metrics for which all the components of the Ricci tensor, except for $R_{11}$, are zero. Although the reduced spacetime is not empty, it is similar to vacuum in the sense that the effective matter satisfies an equation of state which is the generalization of $(ρ+ 3p) = 0$ for "nongravitating matter" in 4D. In Kaluza-Klein gravity these Schwarzschild-like metrics describe the exterior of a spherical star without rotation. In this framework, we generalize the well-known Buchdahl's theorem for perfect fluid spheres whose mass density does not increase outward. Without any additional assumptions, we develop the most general expression for the compactness limit of a star. We provide some numerical values for it, which in principle are observationally testable and allow us to compare and contrast different theories and exteriors. We find that in Kaluza-Klein gravity the compactness limit of a star can be larger than 1/2, without being a black hole: the general-relativistic upper limit $M/R < 4/9$ is increased as we go away from the Schwarzschild vacuum exterior. We show how this limit depends on the number of dimensions of spacetime, and demonstrate that the effects of gravity are stronger in 4D than in any other number of dimensions.

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arXiv2010

Brans-Dicke Cosmology in 4D from scalar-vacuum in 5D

We show that Brans-Dicke (BD) theory in 5D may explain the present cosmic accelerated expansion without recurring to matter fields in 5D or dark energy in 4D. Without making any assumption on the nature of the extra coordinate or the matter content in 5D, here we demonstrate that the vacuum BD field equations in 5D are equivalent, on every hypersurface orthogonal to the extra dimension, to a BD theory in 4D with a self interacting potential and an effective matter field. The potential is not introduced by hand, instead the reduction procedure provides an expression that determines its shape up to a constant of integration. It also establishes the explicit formulae for the effective matter in 4D. In the context of FRW cosmologies, we show that the reduced BD theory gives rise to models for accelerated expansion of a matter-dominated universe which are consistent with current observations and with a decelerating radiation-dominated epoch.

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arXiv2010

Late time cosmic acceleration from vacuum Brans-Dicke theory in 5D

We show that the scalar-vacuum Brans-Dicke equations in 5D are equivalent to Brans-Dicke theory in 4D with a self interacting potential and an effective matter field. The cosmological implication, in the context of FRW models, is that the observed accelerated expansion of the universe comes naturally from the condition that the scalar field is not a ghost, i.e., $ω> - 3/2$. We find an effective matter-dominated 4D universe which shows accelerated expansion if $- 3/2 < ω< - 1$. We study the question of whether accelerated expansion can be made compatible with large values of $ω$, within the framework of a 5D scalar-vacuum Brans-Dicke theory with variable, instead of constant, parameter $ω$. In this framework, and based on a general class of solutions of the field equations, we demonstrate that accelerated expansion is incompatible with large values of $ω$.

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arXiv2009

Effective spacetime from multi-dimensional gravity

We study the effective spacetimes in lower dimensions that can be extracted from a multidimensional generalization of the Schwarzschild-Tangherlini spacetimes derived by Fadeev, Ivashchuk and Melnikov ({\it Phys. Lett,} {\bf A 161} (1991) 98). The higher-dimensional spacetime has $D = (4 + n + m)$ dimensions, where $n$ and $m$ are the number of "internal" and "external" extra dimensions, respectively. We analyze the effective $(4 + n)$ spacetime obtained after dimensional reduction of the $m$ external dimensions. We find that when the $m$ extra dimensions are compact (i) the physics in lower dimensions is independent of $m$ and the character of the singularities in higher dimensions, and (ii) the total gravitational mass $M$ of the effective matter distribution is less than the Schwarzshild mass. In contrast, when the $m$ extra dimensions are large this is not so; the physics in $(4 + n)$ does explicitly depend on $m$, as well as on the nature of the singularities in high dimensions, and the mass of the effective matter distribution (with the exception of wormhole-like distributions) is bigger than the Schwarzshild mass. These results may be relevant to observations for an experimental/observational test of the theory.

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arXiv2009

Static wormholes on the brane inspired by Kaluza-Klein gravity

We use static solutions of 5-dimensional Kaluza-Klein gravity to generate several classes of static, spherically symmetric spacetimes which are analytic solutions to the equation $^{(4)}R = 0$, where $^{(4)}R$ is the four-dimensional Ricci scalar. In the Randall $&$ Sundrum scenario they can be interpreted as vacuum solutions on the brane. The solutions contain the Schwarzschild black hole, and generate new families of traversable Lorenzian wormholes as well as nakedly singular spacetimes. They generalize a number of previously known solutions in the literature, e.g., the temporal and spatial Schwarzschild solutions of braneworld theory as well as the class of self-dual Lorenzian wormholes. A major departure of our solutions from Lorenzian wormholes {\it a la} Morris and Thorne is that, for certain values of the parameters of the solutions, they contain three spherical surfaces (instead of one) which are extremal and have finite area. Two of them have the same size, meet the "flare-out" requirements, and show the typical violation of the energy conditions that characterizes a wormhole throat. The other extremal sphere is "flaring-in" in the sense that its sectional area is a local maximum and the weak, null and dominant energy conditions are satisfied in its neighborhood. After bouncing back at this second surface a traveler crosses into another space which is the double of the one she/he started in. Another interesting feature is that the size of the throat can be less than the Schwarzschild radius $2 M$, which no longer defines the horizon, i.e., to a distant observer a particle or light falling down crosses the Schwarzschild radius in a finite time.

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arXiv2009

4D spacetimes embedded in 5D light-like Kasner universes

We consider spatially homogeneous, anisotropic cosmological models in 5D whose line element can be written as $dS^2 = {\cal{A}}(u, v)du dv - {\cal{B}}_{i j}(u, v)dx^{i}dx^{j}$, $(i, j = 1, 2, 3)$, where $u$ and $v$ are light-like coordinates. In the case where ${\cal{B}}_{i j}$ is diagonal, we construct three families of analytic solutions to the 5D vacuum field equations $R_{AB} = 0$ $ (A, B = 0, 1, 2, 3, 4)$. Among them, there is a family of self-similar homothetic solutions that contains, as a particular case, the so-called light-like Kasner universes. In this work we provide a detailed study of the different types of 4D scenarios that can be embedded in such universes. For the sake of generality of the discussion, and applicability of the results, in our analysis we consider the two versions of non-compactified 5D relativity in vogue, viz., braneworld theory and induced matter theory. We find a great variety of cosmological models in 4D which are anisotropic versions of the FRW ones. We obtain models on the brane with a non-vanishing cosmological term $Λ_{(4)}$, which inflate {\it à la} de Sitter without satisfying the classical false-vacuum equation of state. Using the symmetry of the solutions, we construct a class of non-static vacuum solutions on the brane. We also develop {\it static} pancake-like distributions where the matter is concentrated in a thin surface (near $z = 0$), similar to those proposed by Zel'dovich for the shape of the first collapsed objects in an expanding anisotropic universe. The solutions discussed here can be applied in a variety of physical situations.

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arXiv2009

Levi-Civita spacetimes in multidimensional theories

We obtain the most general static cylindrically symmetric vacuum solutions of the Einstein field equations in $(4 + N)$ dimensions. Under the assumption of separation of variables, we construct a family of Levi-Civita-Kasner vacuum solutions in $(4 + N)$. We discuss the dimensional reduction of the static solutions. Depending on the reduction procedure, they can be interpreted either as a scalar-vacuum generalization of Levi-Civita spacetimes, or as the effective 4D vacuum spacetime outside of an idealized string in braneworld theory.

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arXiv2009

Modern cosmologies from empty Kaluza-Klein solutions in 5D

We show that the empty five-dimensional solutions of Davidson-Sonnenschtein-Vozmediano, {\em Phys. Rev.} {\bf D32} (1985)1330, in the "old" Kaluza-Klein gravity, under appropriate interpretation can generate an ample variety of cosmological models in 4D, which include the higher-dimensional modifications to general relativity predicted by "modern" versions of noncompactified 5D gravity as, e.g., induced-matter and braneworld theories. This is the first time that these solutions are investigated in a systematic way as embeddings for cosmological models in 4D. They provide a different formulation, which is complementary to the approaches used in current versions of 5D relativity.

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arXiv2008

Wave-like Solutions for Bianchi type-I cosmologies in 5D

We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the metric tensor is diagonal and independent of the coordinates for ordinary 3D space. These assumptions lead to three different types of self-similarity in 5D: homothetic, conformal and "wave-like". In this work we present the most general wave-like solutions to the 5D field equations. Using the standard technique based on Campbell's theorem, they generate a large number of anisotropic cosmological models of Bianchi type-I, which can be applied to our universe after the big-bang, when anisotropies could have played an important role. We present a complete review of all possible cases of self-similar anisotropic cosmologies in 5D. Our analysis extends a number of previous studies on wave-like solutions in 5D with spatial spherical symmetry.

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arXiv2008

Self-similar cosmologies in 5D: spatially flat anisotropic models

In the context of theories of Kaluza-Klein type, with a large extra dimension, we study self-similar cosmological models in 5D that are homogeneous, anisotropic and spatially flat. The "ladder" to go between the physics in 5D and 4D is provided by Campbell-Maagard's embedding theorems. We show that the 5-dimensional field equations $R_{AB} = 0$ determine the form of the similarity variable. There are three different possibilities: homothetic, conformal and "wave-like" solutions in 5D. We derive the most general homothetic and conformal solutions to the 5D field equations. They require the extra dimension to be spacelike, and are given in terms of one arbitrary function of the similarity variable and three parameters. The Riemann tensor in 5D is not zero, except in the isotropic limit, which corresponds to the case where the parameters are equal to each other. The solutions can be used as 5D embeddings for a great variety of 4D homogeneous cosmological models, with and without matter, including the Kasner universe. Since the extra dimension is spacelike, the 5D solutions are invariant under the exchange of spatial coordinates. Therefore they also embed a family of spatially {\it inhomogeneous} models in 4D. We show that these models can be interpreted as vacuum solutions in braneworld theory. Our work (I) generalizes the 5D embeddings used for the FLRW models; (II) shows that anisotropic cosmologies are, in general, curved in 5D, in contrast with FLRW models which can always be embedded in a 5D Riemann-flat (Minkowski) manifold; (III) reveals that anisotropic cosmologies can be curved and devoid of matter, both in 5D and 4D, even when the metric in 5D explicitly depends on the extra coordinate, which is quite different from the isotropic case.

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arXiv2008

The equivalence principle in Kaluza-Klein gravity

In four-dimensional general relativity the spacetime outside of an isolated spherical star is described by a unique line element, which is the Schwarzschild metric. As a consequence, the "gravitational" mass and the "inertial" mass of a star are equal to each other. However, theories that envision our world as embedded in a larger universe, with more than four dimensions, permit a number of possible non-Schwarzschild 4D exteriors, which typically lead to {\it different} masses, violating the weak equivalence principle of ordinary general relativity. Therefore, the question arises of whether the violation of this principle, i.e., the equality of gravitational and inertial mass, is a necessary consequence of the existence of extra dimensions. In this paper, in the context of Kaluza-Klein gravity in 5D, we show that the answer to this question is negative. We find a one-parameter family of asymptotically flat non-Schwarzschild static exteriors for which the inertial and gravitational masses are equal to each other, and equal to the Deser-Soldate mass. This family is consistent with the Newtonian weak-field limit as well as with the general-relativistic Schwarzschild limit. Thus, we conclude that the existence of an extra dimension, and the corresponding non-Schwarzschild exterior, does not necessarily require different masses. However, to an observer in 4D, it does affect the motion of test particles in 4D, which is a consequence of the departure from the usual $(4D)$ law of geodesic motion.

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arXiv2008

Static exteriors for nonstatic braneworld stars

We study possible static non-Schwarzschild exteriors for nonstatic spherically symmetric stars in a Randall $&$ Sundrum type II braneworld scenario. Thus, the vacuum region outside the surface of a star is assumed to be a static solution to the equation $^{(4)}R = 0$, where $^{(4)}R $ is the scalar curvature of the 4-dimensional Ricci tensor with spherical symmetry. Firstly, we show that for nonstatic spheres the standard matching conditions are much more restrictive than for static ones; they lead to a specific requirement on the vacuum region outside of a nonstatic star, that is absent in the case of static stars. Secondly, without making any assumption about the bulk, or the material medium inside the star, we prove the following theorem on the brane: for {\it any} nonstatic spherical star, without rotation, there are only two possible static exteriors; these are the Schwarzschild and the "Reissner-Nordstr{ö}m-like" exteriors. This is quite distinct from the case of stars in hydrostatic equilibrium which admit a much larger family of non-Schwarzschild static exteriors.

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arXiv2008

Self-similar cosmologies in 5D: Our universe as a topological separation from an empty 5D Minkowski space

In this paper we find the most general self-similar, homogeneous and isotropic, Ricci flat cosmologies in 5D. These cosmologies show a number of interesting features: (i) the field equations allow a complete integration in terms of one arbitrary function of the similarity variable, and a free parameter; (ii) the three-dimensional spatial surfaces are flat; (iii) the extra dimension is spacelike; (iv) the general solution is Riemann-flat in 5D but curved in 4D, which means that an observer confined to 4D spacetime can relate this curvature to the presence of matter, as determined by the Einstein equations in 4D. We show that these cosmologies can be interpreted, or used, as 5D Riemann-flat embeddings for spatially-flat FRW cosmologies in 4D. In this interpretation our universe arises as a topological separation from an empty 5D Minkowski space, as envisioned by Zeldovich.

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arXiv2007

Embeddings for 4D Einstein equations with a cosmological constant

There are many ways of embedding a 4D spacetime in a given higher-dimensional manifold while, satisfying the field equations. In this work we extend and generalize a recent paper by Mashhoon and Wesson ({\it Gen. Rel. Gravit.} {\bf 39}, 1403(2007)) by showing different ways of embedding a solution of the 4D Einstein equations, in vacuum with a cosmological constant, in a Ricci-flat, as well as in an anti-de Sitter, 5D manifold. These embeddings lead to different physics in 4D. In particular, to non-equivalent cosmological terms as functions of the extra coordinate. We study the motion of test particles for different embeddings and show that there is a complete equivalence between several definitions for the effective mass of test particles measured in 4D, obtained from different theoretical approaches like the Hamilton-Jacobi formalism and the principle of least action. For the case under consideration, we find that the effective mass observed in 4D is the same regardless of whether we consider null or non-null motion in 5D.

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