arXiv subjects

L. C. Garcia de Andrade

Publications and source records attributed to L. C. Garcia de Andrade.

At least 37 records · Page 2Linked to original sources

arXiv2005

Torsion effects on vortex filaments and Hasimoto soliton transformation in magnetars

The role played by torsion of magnetic vortex line curves or filaments, in the equilibrium state of magnetars is investigated. When the magnetars equilibrium equations are written in terms Frenet-Serret frame it is shown that in regions of the magnetic star where the Frenet torsion is constant it induces an oscillation in the vortex filaments. By solving the magnetar equilibrium equation we shown the this behaviour also appears in the magnetic field. The first derivative of the gravitational potential with respect to the arc lenght of the vortex filament is shown to coincide with the Hasimoto soliton transformation of the Schroedinger equation for the constant torsion.

astro-ph↗

arXiv2005

Analogue non-Riemannian black holes in vortical moving plasmas

Analogue black holes in non-Riemannian effective spacetime of moving vortical plasmas described by moving magnetohydrodynamic (MHD) flows. This example is an extension of acoustic torsion recently introduced in the literature (Garcia de Andrade,PRD(2004),7,64004), where now the presence of artificial black holes in moving plasmas is obtained by the presence of an horizon in the non-Riemannian spacetime. Hawking radiation is computed in terms of the background magnetic field and the magnetic permeability. The metric is singular although Cartan analogue torsion is not necessarily singular. The effective Lorentz invariance is shown to be broken due to the presence of effective torsion in strong analogy with the Riemann-Cartan gravitational case presented recently by Kostelecky (PRD 69,2004,105009).

gr-qc↗

arXiv2005

Hawking radiation in moving plasmas

Bi-metricity and Hawking radiation are exhibit in non-relativistic moving magnetohydrodynamics (MHD) plasma medium generating two Riemannian effective spacetimes. The first metric is a flat metric although the speed of "light" is given by a time dependent signal where no Hawking radiation or effective black holes are displayed. This metric comes from a wave equation which the scalar function comes from the scalar potential of the background velocity of the fluid and depends on the perturbation of the magnetic background field. The second metric is an effective spacetime metric which comes from the perturbation of the background MHD fluid. This Riemann metric exhibits a horizon and Hawking radiation which can be expressed in terms of the background constant magnetic field. The effective velocity is given Alfven wave velocity of plasma physics. The effective black hole found here is analogous to the optical black hole in moving dielectrics found by De Lorenci et al [Phys. Rev. D (2003)] where bi-metricity and Hawking radiation in terms of the electric field are found.

gr-qc↗

arXiv2005

Differential Geometric and Topological methods with MHD and plasma physics

Non-solitonic examples of the application of geometrical and topological methods in plasma physics and magnetohydrodynamics (MHD) are given. The first example considers the generalization of magnetic helicity to gravitational torsion loop. The second example considers also the application of this same torsion loop metric to some problems of helical fields in MHD dynamo theory. In the last example a Riemannian magnetic metric is given where the magnetic field itself is present in the diagonal time-independent metric. In this example the MHD equations are shown to be compatible to the geometrical Bianchi identity by making use of Cartan's differential calculus formalism. The Riemann curvature of the helical flow is also obtained.

physics.plasm-ph↗

arXiv2005

Relativistic superfluid hydrodynamics

Relativistic Riemannian superfluid hydrodynamics used in general relativity to investigate superfluids in pulsars is extended to non-Riemannian background spacetime endowed with Cartan torsion. From the Gross-Pitaeviskii (GP) it is shown that in the weak field Cartan torsion approximation, the torsion vector is orthogonal to the superfluid plane wave velocity. Torsion vector is also shown to be aligned along the vortex direction in the superfluid. The background torsion is shown to induce rotation on the fluid as happens with the acoustic torsion in the analogue non-Riemannian non-relativistic superfluid models. The torsion part of the current would be connected to the normal part of the superfluid velocity while the Riemannian part of the velocity would be connected to the superfluid velocity itself. Magnus effect and the rotation of the superfluid are analysed. Since the Kalb-Ramond field is easily associated with torsion our method seems to be equivalent to the vortex-cosmic string relativistic superfluid method developed by Carter and Langlois to investigate rotating neutron stars.

gr-qc↗

arXiv2005

The necessity of non-Riemannian acoustic spacetime in the fluids with vorticity

The necessity of a newly proposed (PRD 70 (2004) 64004) non-Riemannian acoustic spacetime structure called acoustic torsion of sound wave equation in fluids with vorticity are discussed. It is shown that this structure, although not always necessary is present in fluids with vorticity even when the perturbation is rotational. This can be done by solving the Bergliaffa et al (Physica D (2004)) gauge invariant equations for sound, superposed to a general background flow, needs to support a non-Riemannian acoustic geometry in effective spacetime. Bergliaffa et al have previously shown that a Riemannian structure cannot be associated to this gauge invariant general system.

gr-qc↗

arXiv2005

Non-Riemannian acoustic spacetime and Magnus field in rotating Bose-Einstein condensates

The teleparallel $T_{4}$ version of Riemannian geometry of acoustic spacetime in rotating $2-D$ Bose-Einstein condensates (BEC) is investigated. An experiment is proposed on the basis of phonon ray trajectory around a vortex. The deviation geodesic equation may be expressed in terms of Cartan acoustic torsion. The Riemann curvature is computed in terms of rotation of the fluid. The geodesic deviation equation shows that the acoustic torsion acts locally as a diverging lens and the stream lines on opposite sides of the BEC vortex flow apart from each other. We also show that the Magnus field is cancelled when the acoustic torsion coincides with the rotation of the condensate. This effect is equivalent to the Meissner effect in superconductors. It is interesting to note how the teleparallel acoustic spacetime constrains the physical parameters in the BEC. Here we use the term acoustic torsion since in teleparallelism it is derived from the acoustic metric.

cond-mat.stat-mech↗

arXiv2005

Non-Riemannian acoustic spacetime of vortex hydrodynamics in Bose-Einstein condensates

Applications of non-Riemannian acoustic geometries in Bose-Einstein condensates (BEC) are considered. The first is the Minkowski-Cartan irrotational vortex acoustic geometry of nonlinear Schrödinger equations of BEC (Gross-Pitaeviskii (GP) equation). In this model, which is an alternative to the Riemannian acoustic geometry of phonons in BEC, the Cartan acoustic torsion is physically interpreted as the bending of the BEC wave function amplitude. Actually this shows that acoustic torsion is given by the density perturbation of BEC flow as happens in relativistic cosmological fluid spacetimes. The Ricci-Cartan curvature scalar is computed and a torsion singularity is found at the origin of a quantized vortex in BEC. In the second example, a transverse Magnus force is shown to be expressed in terms of acoustic torsion on a teleparallel vortex acoustics geometry.

cond-mat.stat-mech↗

arXiv2005

A teleparallel effective geometry for Einstein's unified field theory

Riemannian and teleparallel geometrical approaches to the investigation of Maxwell electrodynamics shown that a unified field theory of gravitation and electromagnetism a la Einstein can be obtained from a stationary metric. This idea contrasts with the recently proposed pre-metric electrodynamics by Hehl and Obukhov. In the teleparallel case the definition of the electric field is obtained straightforward from the spacetime metric and the orthonormal basis frame of teleparallelism. In this case the only nonvanishing component of Cartan torsion is defined as the effective electric field. In this approach the gravitational potentials or metric coefficients are expressed in terms of the effective or analogous electric and magnetic potentials. Thefore the Maxwell equations in vacuum can be obtained by derivation of this electric field definition as usual. In the Riemannian case we consider an electrostatic spacetime where the Einstein equations in vacuum in the approximation of linear fields. The constraint of Einstein equations in vacuum are shown to lead or to the Coulomb equation or to a singular behaviour on the metric which would represent a kind of effective electrodynamic black hole event horizon.

gr-qc↗

arXiv2005

Non-Riemannian effective spacetime effects on Hawking radiation in superfluids

Riemannian effective spacetime description of Hawking radiation in $^{3}He-A$ superfluids is extended to non-Riemannian effective spacetime. An example is given of non-Riemannian effective geometry of the rotational motion of the superfluid vacuum around the vortex where the effective spacetime Cartan torsion can be associated to the Hawking giving rise to a physical interpretation of effective torsion recently introduced in the literature in the form of an acoustic torsion in superfluid $^{4}He$ (PRD-70(2004),064004). Curvature and torsion singularities of this $^{3}He-A$ fermionic superfluid are investigated. This Lense-Thirring effective metric, representing the superfluid vacuum in rotational motion, is shown not support Hawking radiation when the isotropic $^{4}He$ is restored at far distances from the vortex axis. Hawking radiation can be expressed also in topological solitons (moving domain walls) in fermionic superfluids in non-Riemannian (teleparallel) $(1+1)$ dimensional effective spacetime. A teleparallel solution is proposed where the quasiparticle speed is determined from the teleparallel geometry.

gr-qc↗

arXiv2004

Non-Riemannian acoustic black holes: Hawking radiation and Lorentz symmetry breaking

A non-Riemannian geometrical approach to the investigation of an acoustic black hole in irrotational mean flows, based on the Lighthill vortex sound theory is given. This additional example of analog gravity based on classical fluids is used to investigate the acoustic Lorentz violation. An example is given where the contortion vector is distributed along a ring inside the fluid which can be gravitational analog of the torsion thick string spacetime defect. It is found that the linear background flow velocity approximation, acoustic Lorentz symmetry is breaking by the acoustic Cartan contortion in analogy to the spontaneous gravitational Lorentz breaking in Riemann-Cartan spacetime discovered recently by Kostelecky. We also show that although the acoustic torsion contributes to the fiducial observer acceleration, it is not present in Hawking radiation since is not presnt in the surface gravity of the acoustic black hole.

gr-qc↗

arXiv2004

Riemannian geometry of gravity waves turbulent black hole analogs

The gravity water wave black (GWBH) hole analog discovered by Schutzhold and Unruh (SU) is extended to allow for the presence of turbulent shear flow. The Riemannian geometry of turbulent black holes (BH) analogs in water waves is computed in the case of laminar tirbulent shear flow. The Riemann curvature is constant and the geodesic deviation equation shows that the curvature acts locally as a diverging lens and the stream lines on opposite sides of the analog black hole flow apart from each other. In this case it is shown that the curvature quantities can be expressed in terms of the Newtonian gravitational constant in the ergoregion. The dispersion relation is obtained for the case of constant flow injection.

gr-qc↗

arXiv2004

Non-Riemannian geometry of turbulent acoustic flows and analog gravity

Non-Riemannian geometry of acoustic non-relativistic turbulent flows is irrotationally perturbed generating a acoustic geometry model with acoustic metric and acoustic Cartan contortion. The contortion term is due to nonlinearities in the turbulent fluid. The acoustic curvature and acoustic contortion are given by Dirac delta distributions. Violation of Lorentz invariance due to turbulence is considered and analog gravity is suggested to be linked to planar acoustic domain walls.

gr-qc↗

arXiv2004

Non-Riemannian vortex geometry of rotational viscous fluids and breaking of the acoustic Lorentz invariance

Acoustic torsion recently introduced in the literature (Garcia de Andrade,PRD(2004),7,64004) is extended to rotational incompressible viscous fluids represented by the generalised Navier-Stokes equation. The fluid background is compared with the Riemann-Cartan massless scalar wave equation, allowing for the generalization of Unruh acoustic metric in the form of acoustic torsion, expressed in terms of viscosity, velocity and vorticity of the fluid. In this work the background vorticity is nonvanishing but the perturbation of the flow is also rotational which avoids the problem of contamination of the irrotational perturbation by the background vorticity. The acoustic Lorentz invariance is shown to be broken due to the presence of acoustic torsion in strong analogy with the Riemann-Cartan gravitational case presented recently by Kostelecky (PRD 69,2004,105009). An example of analog gravity describing acoustic metric is given based on the teleparallel loop where the acoustic torsion is given by the Lense-Thirring rotation and the acoustic line element corresponds to the Lense-Thirring metric.

gr-qc↗

arXiv2004

Geometric Phase for Fermionic Quasiparticles Scattering by Disgyration in Superfluids

We consider a Volovik's analog model for description of a topological defects in a superfluid and we investigate the scattering of quasiparticles in this background. The analog of the gravitational Aharonov-Bohm in this system is found. An analysis of this problem employing loop variables is considered and corroborates for the existence of the Aharonov-Bohm effect in this system. The results presented here may be used to study the Aharonov-Bohm effect in superconductors.

gr-qc↗

arXiv2004

Non-Riemannian geometry of vortex acoustics

The concept of acoustic metric introduced previously by Unruh (PRL-1981) is extended to include Cartan torsion by analogy with the scalar wave equation in Riemann-Cartan (RC) spacetime. This equation describes irrotational perturbations in rotational non-relativistic fluids. This physical motivation allows us to show that the acoustic line element can be conformally mapped to the line element of a stationary torsion loop in non-Riemannian gravity. Two examples of such sonic analogues are given. The first is when we choose the static torsion loop in teleparallel gravity. In this case Cartan torsion vector in the far from the vortex approximation is shown to be proportional to the quantum vortex number of the superfluid. Also in this case the torsion vector is shown to be proportional to the superfluid vorticity in the presence of vortices. Torsion loops in RC spacetime does not favor the formation of superfluid vortices. It is suggested that the teleparallel model may help to find a model for superfluid neutron stars vortices based on non-Riemannian gravity.

gr-qc↗

arXiv2004

Holonomy, Aharonov-Bohm effect and phonon scattering in superfluids

In this article we discuss the analogy between superfluids and a spinning thick cosmic string. We use the geometrical approach to obtain the geometrical phases for a phonon in the presence of a vortex. We use loop variables for a geometric description of Aharonov-Bohm effect in these systems. We use holonomy transformations to characterize globally the "space-time" of a vortex and in this point of view we study the gravitational analog of the Aharonov-Bohm effect in this system. We demonstrate that in the general case the Aharonov-Bohm effect has a contribution both from the rotational and the translational holonomy. We study also Berrys quantum phase for phonons in this systems.

gr-qc↗

arXiv2003

Photon mass and cosmological constant bounds from spacetime torsion

Photon mass and Cartan contortion bounds recently obtained from tiny Lorentz violation observations in cosmology are used to find a limit of $λ\le 10^{-4}α$ for the massive photon-torsion dimensionless coupling. Here $α$ represents the fine-structure constant. A gauge invariant Proca electrodynamics in spacetime endowed with torsion in de Sitter spacetime is used to obtain an upper bound for the present value of the cosmological constant given by $Λ\le 10^{-56} cm^{-2}$. This result is obtained in regions of the universe where the photons are massless. A relation between the contortion, photon mass and the radius of the universe is obtained. The Proca electrodynamics with torsion and the radius of the universe allow us to place more stringent bounds for the photon mass of $m_γ{\le} 10^{-44} GeV$ which is only two orders of magnitude lower than the astronomical bounds given by the PARTICLE DATA GROUP (PDG). We also show that charge is locally conserved in de Sitter spacetime with torsion and that plane waves are shown to be damping by contortion inhomogeneities while dispersion is isotropic and therefore Proca-Cartan photons do not violate Lorentz invariance.

astro-ph↗