Linear gravitational waves and electrodynamic formalism in cosmology

The propagation of linear gravitational waves is studied in open and multiply connected Robertson-Walker cosmologies. In order for the group velocity of the gravitational wave packets to coincide with the speed of light, the linear wave equation must be conformally coupled. This opens the possibility of using the electromagnetic formalism. The gravitational analogue to the electromagnetic field tensor is introduced, and a tensorial counterpart to Maxwell's equations on the spacelike 3-slices is derived. The energy-momentum tensor for linear gravitational waves is constructed without averaging procedures, a strictly positive energy density is obtained, and it is shown that the overall energy of a gravitational pulse scales with the inverse of the expansion factor.     

Stability Analysis of Solitary Wave Solutions for Coupled and(2+1)-Dimensional Cubic Klein-Gordon Equations and Their Applications

The searching exact solutions in the solitary wave form of non-linear partial differential equations(PDEs play a significant role to understand the internal mechanism of complex physical phenomena. In this paper, we employ the proposed modified extended mapping method for constructing the exact solitary wave and soliton solutions of coupled Klein-Gordon equations and the(2+1)-dimensional cubic Klein-Gordon(K-G) equation. The Klein-Gordon equation are relativistic version of Schr¨odinger equations, which describe the relation of relativistic energy-momentum in the form of quantized version. We productively achieve exact solutions involving parameters such as dark and bright solitary waves, Kink solitary wave, anti-Kink solitary wave, periodic solitary waves, and hyperbolic functions in which severa solutions are novel. We plot the three-dimensional surface of some obtained solutions in this study. It is recognized that the modified mapping technique presents a more prestigious mathematical tool for acquiring analytical solutions o PDEs arise in mathematical physics.     

Energy velocity and quality factor of poroelastic waves in isotropic media

The energy velocity and Q factor of poroelastic acoustic waves in the context of classical isotropic Biot's theory are revisited. Special attention is paid to the high frequency regime when interphase interaction is viscoelastic. The analogy with viscoelastic behavior is emphasized in derivation of the energy balance equations which relate kinetic energy, potential energy, viscous power dissipation, and elastic energy stored associated with each wave. These lead to exact closed form expressions for the energy velocity and Q factor for both longitudinal and shear waves from energy principles. Most notably, the analysis of the resulting expressions reveals that the energy velocity of both longitudinal and shear waves equals (exceeds) the corresponding phase velocity in the case of the low (full) frequency range theory, and that the exact expression for the Q factor contains an additive correction due to viscoelastic interphase interaction.     

Energy localization in general relativity: A new hypothesis

A new hypothesis for energy localization in general relativity is introduced which is based upon the fact that the energy-momentum conservation laws are devoid of content in vacuum. The vanishing of pseudotensor components forms the basis of coordinate conditions consistent with the above. The implication is that energy is localized where the energy-momentum tensor is nonvanishing. As a consequence, gravitational waves are not carriers of energy in vacuum. A detailed analysis of a Feynman detector interacting with a plane gravitational wave is consistent with the hypothesis. The fact that there has never been a confirmed direct energy transfer to a detector via gravitational radiation is also consistent with the hypothesis.     

On energy transfer by gravitational waves

The solutions of Møller's tetrad equations are found for the three types of exact gravitational waves, for which Møller's energy-momentum complex gives vanishing densities of gravitational energy and energy current.     

Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma. II. Energetic Analysis of Certain Types of Monoenergetic Beam-Plasma Interactions Based on the Čerenkov Resonance Condition

The energy and momentum balance equations for a potential wave in a monoenergetic electron beam-plasma system are considered in the linear approximation, when the wave is in ?erenkov resonance with the beam particles. An energetic analysis of certain types of beam-plasma instabilities is given. It is shown that the energy and momentum balance equations are consistent with the dispersion relation for all unstable waves. From this fact follows that the energy and momentum densities of all linear unstable waves in reactive beam-plasma systems are equal to zero. An interpretation and a possible classification of beam-plasma instabilities are given.     

Heavy ion collisions in AdS5

We study heavy ion collisions at strong ?t Hooft coupling using AdS/CFT correspondence. Heavy ion collisions correspond to gravitational shock wave collisions in AdS₅. We construct the metric in the forward light cone after the collision perturbatively through expansion of Einstein equations in graviton exchanges. We obtain an analytic expression for the metric including all-order graviton exchanges with one shock wave, while keeping the exchanges with another shock wave at the lowest order. We read off the corresponding energy-momentum tensor of the produced medium. Unfortunately this energy-momentum tensor does not correspond to ideal hydrodynamics, indicating that higher order graviton exchanges are needed to construct the full solution of the problem. We also show that shock waves must completely stop almost immediately after the collision in AdS₅, which, on the field theory side, corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. Finally, we perform trapped surface analysis of the shock wave collisions demonstrating that a bulk black hole, corresponding to ideal hydrodynamics on the boundary, has to be created in such collisions, thus constructing a proof of thermalization in heavy ion collisions at strong coupling.     

On the momentum of potential waves

Protracted discussions on concepts like the momentum of electromagnetic waves in matter and the pressure of sound indicate that the interpretation of the momentum balance in non-relativistic physics can be less clear than that of the energy balance. It is shown that this can be understood from the theory of a special class of wave equations, called potential waves.     

Electromagnetic energy, momentum, and angular momentum in an inhomogeneous linear dielectric

In a previous work, Optics Communications 284 (2011) 2460-2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy-momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of time, which essentially represents a mechanically rigid dielectric medium due to external constraints. Using continuity equations for energy density and for Gordon momentum density, we construct a symmetric energy-momentum matrix, whose four-divergence is equal to a generalized Helmholtz force density four-vector. Assuming that the energy-momentum matrix has tensor transformation properties under a symmetry group of space-time coordinate transformations, we derive the global conservation laws for the total energy, momentum, and angular momentum.     

The radiation impedance and the energy partition among wave fields generated by a normal force strip radiator on isotropic solid surface

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Inconsistency of nonlinear second-order equations of motion of classical charges

Problems of second-order equations of motion of elementary classical charges are discussed. Inconsistency of energy-momentum balance is pointed out. In particular, it is shown, probably for the first time, that Eliezer's equation does not conserve energy. The results favor the third-order equation of Lorentz-Dirac.     

The velocity of magnetohydrodynamic waves in general relativity

The energy-momentum tensor for a perfect fluid with infinite conductivity is modified slightly by attributing a proper energy content to a field of tension, as proposed by Cattaneo, for a perfect nonconducting fluid, and it is shown that with this modification the velocities of the hydrodynamic waves in the fluid do not exceed C. This contrasts with the standard theory in which a lower limit must be placed on the compressibility of the fluid to prevent the velocity of the ‘fast’ hydrodynamic wave fron exceeding c. The velocity of the Alfvén wave is changed only slightly and is always less than c as in the standard theory.     

Heisenberg Group and Energy-Momentum Conservative Law in de-Sitter Spaces In Memory of the 100th Anniversary of Einstein‘s Special Relativity and the 70th Anniversary of Dirac‘s de-Sitter Spaces and Their Boundaries

In 1935 Dirac established the physical wave equations in the de-Sitter spaces but neither energy-momentum operators nor their conservative laws were given. In this article it is proved that in the de-Sitter group there is a subgroup group isomorphic to the Heisenberg group and the generators of this groups are the energy-momentum operators which obey a conservative law.     

Full pump energy conversion at parametric amplification

The full conversion of the modulated wave energy is shown to be possible and can be reached at mutually simple conformity between the spatial-temporal, modulation forms of interaction waves.     

Heisenberg Group and Energy-Momentum Conservative Law in de-Sitter Spaces—— In Memory of the 100th Anniversary of Einstein＇s Special Relativity and the 70th Anniversary of Dirac＇s de-Sitter Spaces

In 1935 Dirac established the physical wave equations in the de-Sitter spaces but neither energy-momentum operators nor their conservative laws were given. In this article it is proved that in the de-Sitter group there is a subgroup group isomorphic to the Heisenberg group and the generators of this groups are the energy-momentum operators which obey a conservative law.     

Charged dilaton,energy, momentum and angular-momentum in teleparallel theory equivalent to general relativity

We apply the energy-momentum tensor to calculate energy, momentum and angular-momentum of two different tetrad fields. This tensor is coordinate independent of the gravitational field established in the Hamiltonian structure of the teleparallel equivalent of general relativity (TEGR). The spacetime of these tetrad fields is the charged dilaton. Our results show that the energy associated with one of these tetrad fields is consistent, while the other one does not show this consistency. Therefore, we use the regularized expression of the gravitational energy-momentum tensor of the TEGR. We investigate the energy within the external event horizon using the definition of the gravitational energy-momentum. PACS 04.70.Bw; 04.50.+h; 04.20.-Jb     

Nonlinear Theory of the Plasma Wave Excitation in a Bounded Beam-Plasma System

The excitation of symmetric and antisymmetric plasma waves by a beam layer that moves within a homogeneous plasma enclosed by a metallic wall was dealt with theoretically. Investigations were carried out for the magnetic field free case and for a magnetized electron beam. In the latter case, the beam electrons are assumed to be unable to move in the perpendicular direction. The theoretical model bases upon an extension of the well known single wave theory to a two-dimensional beam-plasma system. Special emphasis should be paid to the fact that the perpendicular wave profile of the excited waves was determined self-consistently. Energy and momentum balance equations are derived for this system. The theoretical method outlined in this paper which is based on a Green's-function technique can be extended easily to three-dimensional systems or to beam-plasma systems with other boundary conditions. The main features of the saturation process of the basic unstable wave types are discussed. Several interesting effects were found in the magnetic field free case: (i) numerical solutions describe an increasing steepening of the wave amplitudes in perpendicular direction near the center of the system for the symmetric potential wave; (ii) for the antisymmetric wave, a smoothing tendency was found in the development of the perpendicular wave potential profile; (iii) spatial separation of the slow and fast beam electrons was observed; (iv) it is shown for the antisymmetric potential wave type that, under certain conditions, a very efficient beam particle retardation mechanism occurs which is connected with a strong reduction of the formation of a fast particle group; (v) generally it was shown that the conversion of the kinetic energy of the beam electrons into the plasma wave energy may be more effective as compared with the case of the magnetized beam.     

Existence of perturbed solitary wave solutions to a model equation for water waves

We prove the existence of travelling wave solutions to a fifth order partial differential equation, which is a formal asymptotic approximation for water waves with surface tension. These travelling waves are arbitrarily small perturbations of solitary waves, but are not solitary waves themselves, because they approach small amplitude oscillations for large values of the independent variable. This result suggests that for Bond numbers less than one third, there are branches of travelling wave solutions to the water wave equations, which are perturbations of supercritical elevation solitary waves, and which bifurcate from Froude number one and Bond number one third.     

Displaced phase-amplitude variables for waves on finite background

Wave amplification in nonlinear dispersive wave equations may be caused by nonlinear focussing of waves from a certain background. In the model of nonlinear Schrödinger equation we will introduce a transformation to displaced phase-amplitude variables with respect to a background of monochromatic waves. The potential energy in the Hamiltonian then depends essentially on the phase. Looking as a special case to phases that are time independent, the oscillator equation for the signal at each position becomes autonomous, with the change of phase with position as only driving force for a spatial evolution towards extreme waves. This is observed to be the governing process of wave amplification in classes of already known solutions of NLS, namely the Akhmediev-, Ma- and Peregrine-solitons. We investigate the case of the soliton on finite background in detail in this Letter as the solution that descibes the complete spatial evolution of modulational instability from background to extreme waves.