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.     

狭窄波束型高频引力辐射与电磁场的作用效应

从弱引力场的Einstein-Maxwell方程出发,讨论了晶体空间阵列的狭窄波束型高频引力辐射与电磁场的作用效应,并给出了扰动解。计算表明,在TT(Transvese Traceless)坐标系中,最优辐射方向的引力波束是纯十型极化的,并可使同频的电磁波产生倍频的扰动效应,使静态电磁场产生与时间成线性关系的累积扰动效应。对于任意方向上的引力辐射波束,在垂直于引力波矢的平面内仍然是纯十型极化的。在高频辐射和实验室典型尺度条件下,TT坐标系与Fermi坐标系的差异是可以忽略的。 关键词：     

Inflationary Brans-Dicke universe andG

In a recent paper, Mathiazhagan and Johri reduced the field equations for an isotropic, homogeneous, and almost flat universe with a constant vacuum-energy density by Brans-Dicke theory to a pair of coupled differential equations. They also obtained a particular solution of these equations. Further, they used this particular solution of the equations to estimate the value of the gravitational constant. Here we obtain the complete set of solutions of the above-mentioned coupled differential equations and improved the estimate of Mathiazhagan and Johri of the gravitational constant.     

Quantized fields propagating in plane-wave spacetimes

This paper contains an account of the interaction of a quantized massive scalar field with the classicalc number gravitational field of a plane sandwich wave of arbitrary profile and polarization. It is shown that the time varying gravitational field of the wave produces no particles and the Feynman propagator for the problem is calculated exactly. This is used to show that any reasonable regularization of the vacuum expectation value of the energy momentum tensor of the field must vanish. This means that a gravitational wave far from its source will propagate without hindrance by quantum effects.     

Generation of gravitational radiation in dusty plasmas and supernovae

We present a novel nonlinear mechanism for exciting a gravitational radiation pulse (or a gravitational wave) by dust magnetohydrodynamic (DMHD) waves in dusty astrophysical plasmas. We derive the relevant equations governing the dynamics of nonlinearly coupled DMHD waves and a gravitational wave (GW). The system of equations is used to investigate the generation of a GW by compressional Alfvén waves in a type II supernova. The growth rate of our nonlinear process is estimated, and the results are discussed in the context of the gravitational radiation accompanying supernova explosions.     

The second order spin-2 system in flat space near space-like and null-infinity

In previous work, the numerical solution of the linearized gravitational field equations near space-like and null-infinity was discussed in the form of the spin-2 zero-rest-mass equation for the perturbations of the conformal Weyl curvature. The motivation was to study the behavior of the field and properties of the numerical evolution of the system near infinity using Friedrich’s conformal representation of space-like infinity as a cylinder. It has been pointed out by H.O. Kreiss and others that the numerical evolution of a system using second order wave equations has several advantages compared to a system of first order equations. Therefore, in the present paper we derive a system of second order wave equations and prove that the solution spaces of the two systems are the same if appropriate initial and boundary data are given. We study the properties of this system of coupled wave equations in the same geometric setting and discuss the differences between the two approaches.     

Motion of an ideal fluid in the field of a plane gravitational wave

An exact solution of the equations of relativistic hydrodynamics is found which describes the motion of an initially uniform ideal fluid in the field of a plane gravitational wave of arbitrary amplitude and polarization. For all solutions we find that the pressure and energy density develop singularities on the singular surface, and the velocity of the fluid in the direction of propagation of the gravitational wave approaches the speed of light. In the case of the equation of state =p, the solution becomes intrinsically unstable and describes the generation of sound waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 96–99, November, 1982.     

Wave coupling theory of quadratic electro-optic effect and its applications

Wave coupling theory of quadratic electro-optic effect is developed by considering the third-order nonlinearity as a perturbation in lossless nonmagnetic centrosymmetric medium. A general solution of the resultant equations is given to describe the quadratic electro-optic effect for the electromagnetic wave propagating along an arbitrary direction with applied external electric field. The effect of the polarization state on electro-optic coupling is studied in paraelectric phase KLTN crystals. A novel application of wave coupling theory of quadratic effect is described, namely polarization rotator, which can rotate the polarization of the electromagnetic wave with an arbitrary angle.     

Time-dependent solutions with localized energy of the Einstein system of equations and a nonlinear scalar field

A soliton-like time-dependent solution in the form of a running wave is derived of a self-consistent system of the gravitational field equations of Einstein and Born-Infeld type of equations of a nonlinear scalar field in a conformally flat metric. This solution is localized in space and possesses a localized energy. It is shown that both the gravitational field and the nonlinearity of the scalar field are essential to the presence of such a localized solution. In recent years various classical particle models have been widely discussed which are static or time-independent solutions of nonlinear equations with localization in space and which possess a finite field energy. In particular, soliton solutions [1], solutions in the form of eddies [2], and so on have been derived and investigated. All these solutions were treated in a flat space-time. It is of interest to derive the analogous particle-like solutions with the gravitational field taken into account; in particular it is of interest to investigate the roles of the gravitational field in connection with the formation of localized objects. These problems have been discussed in [3] in the static case. We will present below a soliton-like time-dependent solution in the form of a solitary running wave as an example of the inter-action of a Born-Infeld type of nonlinear scalar field and an Einstein gravitational field in a conformally flat metric.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 12–17, May, 1979.     

Colliding Plane Waves in Einstein–Maxwell Theory

Recently, a simple solution of the vacuum Einstein–Maxwell field equations was given describing a plane electromagnetic shock wave sharing its wave front with a plane gravitational impulse wave. We present here an exact solution of the vacuum Einstein–Maxwell field equations describing the head-on collision of such a wave with a plane gravitational impulse wave. The solution has the Penrose–Khan solution and a solution obtained by Griffiths as separate limiting cases.     

Gravitational Faraday Effect Produced by a Ring Laser

Using the linearized Einstein gravitational field equations and the Maxwell field equations it is shown that the plane of polarization of an electromagnetic wave is rotated by the gravitational field created by the electromagnetic radiation of a ring laser. It is further shown that this gravitational Faraday effect shares many of the properties of the standard electromagnetic Faraday effect. An experimental arrangement is then suggested for the observation of this gravitational Faraday effect induced by the ring laser.     

f(R,L m ) gravity

We generalize the f(R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian L _m . We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert–Einstein Lagrange density are also derived.     

Nonlinear theory of the compressible gas flows over a nonuniform boundary in the gravitational field in the shallow-water approximation

A set of equations is derived for the motion of a compressible ideal gas over a nonuniform boundary in the gravitational field in the shallow-water approximation. Classical simple waves are shown not to be the solutions to this set of equations. Generalized simple waves are found to exist only in the case of a linear underlying-surface profile. All continuous and discontinuous solutions are obtained in an explicit form for the case of the boundary in the form of an inclined plane, and an analytical solution is found for the problem of the decay of an arbitrary discontinuity. This solution consists of four wave configurations. Necessary and sufficient conditions are determined for the existence of each configuration.     

The variant of post-Newtonian mechanics with generalized fractional derivatives

In this article, we investigate mathematically the variant of post-Newtonian mechanics using generalized fractional derivatives. The relativistic-covariant generalization of the classical equations for gravitational field is studied. The equations (i) match the weak Newtonian limit on the moderate scales and (ii) deliver a potential higher than Newtonian on certain large-distance characteristic scales. The perturbation of the gravitational field results in the tiny secular perihelion shift and exhibits some unusual effects on large scales. The general representation of the solution for the fractional wave equation is given in the form of retarded potentials. The solutions for the Riesz wave equation and classical wave equation are clearly distinctive in an important sense. The hypothetical gravitational Riesz wave demonstrates the space diffusion of the wave at the scales of metric constant. The diffusion leads to the blur of the peak and disruption of the sharp wave front. This contrasts with the solution of the D'Alembert classical wave equation, which obeys the Huygens principle and does not diffuse.     

Letter: An Exact Solution for the Fluctuations of an FRW Cosmology with n Scalar Fields, for an Arbitrary Potential

In this work we rigorously study the fluctuations in FRW models coupled with n neutral scalar fields, minimally coupled to the gravitational field. We find the exact solutions and the asymptotic behavior for the fluctuation around the critical point of the background for an arbitrary potential.     

Generalized wave coupling theory of linear electro-optic effect in absorbent medium

Starting from Maxwell’s equations and considering the linear electro-optic effect as a perturbation, we present a generalized wave coupling theory of linear electro-optic effect in absorbent medium. We give the rigorous solution of the resultant equations for a light wave propagating along any direction with an external dc electric field along an arbitrary direction. As an application, we use the theory to discuss the influence of absorption on the light wave in a KTP crystal. The results demonstrate that the absorption coefficients influence not only the amplitude but also the phase of the light wave.     

Gravitational Radiation and Nonlocal Electrodynamics

A model of nonlocal response of a medium with an initially constant and homogeneous magnetic field acted upon by a planar gravitational wave is constructed on the basis of a covariant formulation of integral constitutive equations. The model is studied in detail and the problem of anomalous behavior of the response of the given electrodynamic system to a gravitational-wave action is discussed.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 27–33, April, 2005.     

Pauli equation for a particle in metric and electromagnetic fields

A Pauli theory (Pauli equation and definition of probability current and density) for a particle in weak metric and arbitrary electromagnetic fields is treated. To formulate non-relativistic quantum mechanical problems in arbitrary electromagnetic fields and weak metrics (non-inertial systems, gravitational fields which are distant fields of arbitrary distribution of masses, gravitational waves) it is not necessary to make use of the general-relativistic Dirac equation. Close analogies to the known Pauli theory with electromagnetic fields exist. For different metric fields the corresponding Hamiltonians are given. For quantum systems (H-atoms) which are disturbed by a homogeneous gravitational field and a gravitational wave the resulting shift of energy levels and the transition probability is calculated.