In this paper the possible geodesic completeness of an electromagnetic dipole wormhole is studied... more In this paper the possible geodesic completeness of an electromagnetic dipole wormhole is studied in detail. The space-time contains a curvature singularity and belongs to a class of solutions to the Einstein-Maxwell equations with a coupled scalar field. Specifically, a numerical analysis is performed to examine congruences of null geodesics that are directed toward the singularity. The results found here show that, depending on the strength of the coupling between the scalar and electromagnetic fields, the wormhole can be either geodesically incomplete or complete. We then focus on those wormholes that are geodesically complete and study the geometry of the neighborhood of their singularity using Kaluza-Klein theory in a five-dimensional space-time. This process allows us to provide a possible explanation of the completeness of geodesics despite unbounded curvature.
Using a generalized Madelung transformation, we derive the hydrodynamic representation of the Dir... more Using a generalized Madelung transformation, we derive the hydrodynamic representation of the Dirac equation in arbitrary curved space-times coupled to an electromagnetic field. We obtain Dirac–Euler equations for fermions involving a continuity equation and a first integral of the Bernoulli equation. Comparing between the Dirac and Klein–Gordon equations we obtain the balance equation for fermion particles. We also use the correspondence between fermions and bosons to derive the hydrodynamic representation of the Weyl equation which is a chiral form of the Dirac equation.
In a previous work [1] it was shown that by considering the quantum nature of the gravitational f... more In a previous work [1] it was shown that by considering the quantum nature of the gravitational field mediator, it is possible to introduce the momentum energy of the graviton into the Einstein equations as an effective cosmological constant. The Compton Mass Dark Energy (CMaDE) model proposes that this momentum can be interpreted as dark energy, with a Compton wavelength given by the size of the observable universe RH, implying that the dark energy varies depending on this size. The main result of this previous work is the existence of an effective cosmological constant Λ = 2π2/λ2 that varies very slowly, being λ = (c/H0)RH the graviton Compton wavelength. In the present work we use that the dark energy density rate is given by ΩΛ = 2π2/3/RH2 , it only has the curvature Ωk as a free constant and depends exclusively on the radiation rate Ωr. Using Ωr = 9.54×10−5, the theoretical prediction for a flat universe of the dark energy rate is ΩΛ = 0.6922. We perform a general study for a n...
In this work we study the local behavior of geodesics in the neighborhood of a curvature singular... more In this work we study the local behavior of geodesics in the neighborhood of a curvature singularity contained in stationary and axially symmetric space–times. Apart from these properties, the metrics we shall focus on will also be required to admit a quadratic first integral for their geodesics. In particular, we search for the conditions on the geometry of the space–time for which null and time-like geodesics can reach the singularity. These conditions are determined by the equations of motion of a freely-falling particle. We also analyze the possible existence of geodesics that do not become incomplete when encountering the singularity in their path. The results are stated as criteria that depend on the inverse metric tensor along with conserved quantities such as energy and angular momentum. As an example, the derived criteria are applied to the Plebański–Demiański class of space–times. Lastly, we propose a line element that describes a wormhole whose curvature singularities are...
In this work we wonder if there is a way to generate a wormhole (WH) in nature using "normal" mat... more In this work we wonder if there is a way to generate a wormhole (WH) in nature using "normal" matter. In order to give a first answer to this question, we study a massless scalar field coupled to an electromagnetic one (dilatonic field) with an arbitrary coupling constant, as source of gravitation. We obtain an exact solution of the Einstein equations using this source that represents a magnetized rotating WH. This space-time has a naked ring singularity, probably untouchable as in [18], but otherwise regular. The WH throat lies on the disc bounded by the ring singularity, which keeps the throat open without requiring exotic matter, that means, satisfying all the energy conditions. After analyzing the geodesic motion and the tidal forces we find that a test particle can go through the WH without troubles.
We analize the properties of a Kerr-like wormhole supported by phantom matter, which is an exact ... more We analize the properties of a Kerr-like wormhole supported by phantom matter, which is an exact solution of the Einstein-phantom field equations with two parameters: mass and scalar field charge. The solution has a naked ring singularity which is unreachable to null geodesics falling freely from outside. Similarly to Roger Penrose's cosmic censorship, here we show that a naked singularity can be fully protected by the intrinsic properties of the wormhole's spacetime.
We study a solution of the field equations for dilatonic gravity and obtain its post-post-newtoni... more We study a solution of the field equations for dilatonic gravity and obtain its post-post-newtonian limit. It turns out that terms to this and higher orders in the expansion may become important in strong gravitational fields, even though the post-newtonian limit coincides with that of General Relativity. This suggests that strong gravitational fields can only be studied by exact solutions
We investigate Gaussian warped five-dimensional thick braneworlds. Identification of the graviton... more We investigate Gaussian warped five-dimensional thick braneworlds. Identification of the graviton's wave function (squared) in the extra-dimension with a probability distribution function leads to a straightforward probabilistic interpretation of braneworlds. The extra-coordinate $y$ is regarded as a Gaussian-distributed random variable. Hence, all of the field variables and operators which depend on $y$ are, also, randomly distributed. Four-dimensional measurable (macroscopic) quantities are identified with the corresponding averaged values over the Gaussian distribution. The present scenario represents a new phenomenological approach to smooth thick branes which can not be obtained through 'smearing out' Randall-Sundrum-like (thin) braneworlds.
A methodology for integrating the chiral equation (ρg,zg−1),z̄+ (ρg,z̄g−1),z=0 is developed, when... more A methodology for integrating the chiral equation (ρg,zg−1),z̄+ (ρg,z̄g−1),z=0 is developed, when g is a matrix of the SL(N,R) group. In this work the ansätze g=g(λ) where λ satisfy the Laplace equation and g=g(λ,τ) are made, where λ and τ are geodesic parameters of an arbitrary Riemannian space. This reduces the chiral equation to an algebraic problem and g can be obtained by integrating a homogeneous linear system of differential equations. As an example of the first ansatz, all the matrices for N=3 and one example for N=8, which corresponds to exact solutions of the d=5 and d=10 Kaluza–Klein theory, respectively are given. For the second ansatz the chiral equations are integrated for the subgroups SL(2,R), SO(2,1R), Sp(2,R), and the Abelian subgroups.
Applying the harmonic map ansatz we find new classes of SU(N) and SO(N) chiral fields. We write t... more Applying the harmonic map ansatz we find new classes of SU(N) and SO(N) chiral fields. We write the corresponding one-dimensional subgroups of SU(N) and SO(N) chiral fields in terms of one and two harmonic maps and the corresponding two-dimensional subgroups in terms of SU(2) and SO(3) chiral fields. In other words, we reduce the SU(N) and SO(N) chiral equations to harmonic maps in one- and two-dimensional spaces.
In this paper the possible geodesic completeness of an electromagnetic dipole wormhole is studied... more In this paper the possible geodesic completeness of an electromagnetic dipole wormhole is studied in detail. The space-time contains a curvature singularity and belongs to a class of solutions to the Einstein-Maxwell equations with a coupled scalar field. Specifically, a numerical analysis is performed to examine congruences of null geodesics that are directed toward the singularity. The results found here show that, depending on the strength of the coupling between the scalar and electromagnetic fields, the wormhole can be either geodesically incomplete or complete. We then focus on those wormholes that are geodesically complete and study the geometry of the neighborhood of their singularity using Kaluza-Klein theory in a five-dimensional space-time. This process allows us to provide a possible explanation of the completeness of geodesics despite unbounded curvature.
Using a generalized Madelung transformation, we derive the hydrodynamic representation of the Dir... more Using a generalized Madelung transformation, we derive the hydrodynamic representation of the Dirac equation in arbitrary curved space-times coupled to an electromagnetic field. We obtain Dirac–Euler equations for fermions involving a continuity equation and a first integral of the Bernoulli equation. Comparing between the Dirac and Klein–Gordon equations we obtain the balance equation for fermion particles. We also use the correspondence between fermions and bosons to derive the hydrodynamic representation of the Weyl equation which is a chiral form of the Dirac equation.
In a previous work [1] it was shown that by considering the quantum nature of the gravitational f... more In a previous work [1] it was shown that by considering the quantum nature of the gravitational field mediator, it is possible to introduce the momentum energy of the graviton into the Einstein equations as an effective cosmological constant. The Compton Mass Dark Energy (CMaDE) model proposes that this momentum can be interpreted as dark energy, with a Compton wavelength given by the size of the observable universe RH, implying that the dark energy varies depending on this size. The main result of this previous work is the existence of an effective cosmological constant Λ = 2π2/λ2 that varies very slowly, being λ = (c/H0)RH the graviton Compton wavelength. In the present work we use that the dark energy density rate is given by ΩΛ = 2π2/3/RH2 , it only has the curvature Ωk as a free constant and depends exclusively on the radiation rate Ωr. Using Ωr = 9.54×10−5, the theoretical prediction for a flat universe of the dark energy rate is ΩΛ = 0.6922. We perform a general study for a n...
In this work we study the local behavior of geodesics in the neighborhood of a curvature singular... more In this work we study the local behavior of geodesics in the neighborhood of a curvature singularity contained in stationary and axially symmetric space–times. Apart from these properties, the metrics we shall focus on will also be required to admit a quadratic first integral for their geodesics. In particular, we search for the conditions on the geometry of the space–time for which null and time-like geodesics can reach the singularity. These conditions are determined by the equations of motion of a freely-falling particle. We also analyze the possible existence of geodesics that do not become incomplete when encountering the singularity in their path. The results are stated as criteria that depend on the inverse metric tensor along with conserved quantities such as energy and angular momentum. As an example, the derived criteria are applied to the Plebański–Demiański class of space–times. Lastly, we propose a line element that describes a wormhole whose curvature singularities are...
In this work we wonder if there is a way to generate a wormhole (WH) in nature using "normal" mat... more In this work we wonder if there is a way to generate a wormhole (WH) in nature using "normal" matter. In order to give a first answer to this question, we study a massless scalar field coupled to an electromagnetic one (dilatonic field) with an arbitrary coupling constant, as source of gravitation. We obtain an exact solution of the Einstein equations using this source that represents a magnetized rotating WH. This space-time has a naked ring singularity, probably untouchable as in [18], but otherwise regular. The WH throat lies on the disc bounded by the ring singularity, which keeps the throat open without requiring exotic matter, that means, satisfying all the energy conditions. After analyzing the geodesic motion and the tidal forces we find that a test particle can go through the WH without troubles.
We analize the properties of a Kerr-like wormhole supported by phantom matter, which is an exact ... more We analize the properties of a Kerr-like wormhole supported by phantom matter, which is an exact solution of the Einstein-phantom field equations with two parameters: mass and scalar field charge. The solution has a naked ring singularity which is unreachable to null geodesics falling freely from outside. Similarly to Roger Penrose's cosmic censorship, here we show that a naked singularity can be fully protected by the intrinsic properties of the wormhole's spacetime.
We study a solution of the field equations for dilatonic gravity and obtain its post-post-newtoni... more We study a solution of the field equations for dilatonic gravity and obtain its post-post-newtonian limit. It turns out that terms to this and higher orders in the expansion may become important in strong gravitational fields, even though the post-newtonian limit coincides with that of General Relativity. This suggests that strong gravitational fields can only be studied by exact solutions
We investigate Gaussian warped five-dimensional thick braneworlds. Identification of the graviton... more We investigate Gaussian warped five-dimensional thick braneworlds. Identification of the graviton's wave function (squared) in the extra-dimension with a probability distribution function leads to a straightforward probabilistic interpretation of braneworlds. The extra-coordinate $y$ is regarded as a Gaussian-distributed random variable. Hence, all of the field variables and operators which depend on $y$ are, also, randomly distributed. Four-dimensional measurable (macroscopic) quantities are identified with the corresponding averaged values over the Gaussian distribution. The present scenario represents a new phenomenological approach to smooth thick branes which can not be obtained through 'smearing out' Randall-Sundrum-like (thin) braneworlds.
A methodology for integrating the chiral equation (ρg,zg−1),z̄+ (ρg,z̄g−1),z=0 is developed, when... more A methodology for integrating the chiral equation (ρg,zg−1),z̄+ (ρg,z̄g−1),z=0 is developed, when g is a matrix of the SL(N,R) group. In this work the ansätze g=g(λ) where λ satisfy the Laplace equation and g=g(λ,τ) are made, where λ and τ are geodesic parameters of an arbitrary Riemannian space. This reduces the chiral equation to an algebraic problem and g can be obtained by integrating a homogeneous linear system of differential equations. As an example of the first ansatz, all the matrices for N=3 and one example for N=8, which corresponds to exact solutions of the d=5 and d=10 Kaluza–Klein theory, respectively are given. For the second ansatz the chiral equations are integrated for the subgroups SL(2,R), SO(2,1R), Sp(2,R), and the Abelian subgroups.
Applying the harmonic map ansatz we find new classes of SU(N) and SO(N) chiral fields. We write t... more Applying the harmonic map ansatz we find new classes of SU(N) and SO(N) chiral fields. We write the corresponding one-dimensional subgroups of SU(N) and SO(N) chiral fields in terms of one and two harmonic maps and the corresponding two-dimensional subgroups in terms of SU(2) and SO(3) chiral fields. In other words, we reduce the SU(N) and SO(N) chiral equations to harmonic maps in one- and two-dimensional spaces.
Uploads
Papers by Tonatiuh Matos