A plane symmetric solution of Einstein's field equations of general relativity containing zero-rest-mass scalar fields

An exact static solution of Einstein's field equations of general relativity in the presence of zero-rest-mass scalar fields has been obtained when both the metric tensor gijand the zero-rest-mass scalar field φexhibit plane symmetry in the sense of Taub [9]. Our solution generalizes the empty space-time solution with plane symmetry previously obtained by Taub to the situation when static zero-rest-mass scalar fields are present. The static plane symmetric solutoins of Einstein's field equations in the presence of massive scalar fields, and the difference between the massless and non-massless scalar fields are being investigated, and will be published separately later on. We also hope to discuss non-static plane symmetric solutions of Einstein's field equations in the presence of scalar fields in future.     

Ideal fluid with short-range scalar interactions in the field of a plane gravitational wave

An exact solution of the self-consistent equations of relativistic hydrodynamics and the scalar field equation is obtained. The solution describes motion of a fluid with short-range scalar interactions in the field of a plane gravitational wave.     

STATIC SPHERICALLY SYMMETRIC SOLUTION OF EINSTEIN GRAVITY COUPLED TO ELECTRO-MAGNETIC AND SCALAR FIELDS

The static spherically symmetric solution of Einstein gravity coupled to electromagnetic and scalar fields is obtained under the consideration of the self-gravitational interaction of the electromagnetic and scalar fields, which is singularity-free and stable.     

The Exact Solution for the Dirac Equation with the Cornell Potential

An analytical solution of the Dirac equation with a Cornell potential, with identical scalar and vectorial parts, is presented. The solution is obtained by using the linear potential solution, related to Airy functions, multiplied by another function to be determined. The energy levels are obtained and we notice that they obey a band structure.     

Self-gravitating scalar field with cubic nonlinearity

For a self-gravitating massless conformally invariant scalar field a solution is obtained to the Einstein equations for which the geometry of space-time remains arbitrary. For a scalar field with cubic nonlinearity, a static solution to the Einstein equations possessing plane symmetry is found. A cosmological model with nonlinear scalar field in the class of conformally flat Friedmann metrics is investigated. An example is given of an exact solution to the equations of the gravitational field with singularity in the infinite past.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 18–22, December, 1980.     

Propagation of Scalar Fields in a Plane Symmetric Spacetime

The present article deals with solutions for a minimally coupled scalar field propagating in a static plane symmetric spacetime. The considered metric describes the curvature outside a massive infinity plate and exhibits an intrinsic naked singularity (a singular plane) that makes the accessible universe finite in extension. This solution can be interpreted as describing the spacetime of static domain walls. In this context, a first solution is given in terms of zero order Bessel functions of the first and second kind and presents a stationary pattern which is interpreted as a result of the reflection of the scalar waves at the singular plane. This is an evidence, at least for the massless scalar field, of an old interpretation given by Amundsen and Grøn regarding the behaviour of test particles near the singularity. A second solution is obtained in the limit of a weak gravitational field which is valid only far from the singularity. In this limit, it was possible to find out an analytic solution for the scalar field in terms of the Kummer and Tricomi confluent hypergeometric functions.     

Exact Solutions of Klein-Gordon Equation with Exponential Scalar and Vector Potentials

We obtain the exact analytical solution of the Klein-Gordon equation for the exponential vector and scalar potentials by using the asymptotic iteration method. For the scalar potential greater than the vector potential case, the exact bound state energy eigenvalues and corresponding eigenfunctions are presented. The bound state eigenfunction solutions are obtained in terms of the confluent hypergeometric functions.     

Quantization of scalar field in cosmic spaces

Equations of scalar field are constructed by the method of embedding in conformally planar cosmic spaces of the general relativity theory (GRT). The equations are linear relative to the scalar field, which, on the one hand, enables one to regard the permutation function as a four-dimensional radially symmetric solution of the equation of the scalar field, and on the other hand, as a commutator of the wave solutions of the field; in this way the quantization laws are determined for the Fourier amplitudes of the solutions of the equations for the meson field. The wave solution of the scalar meson field is found in the conformally planar GRT space, and the permutation function is obtained as their commutator.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 75–79, March, 1977.     

平面对称标量场的静态时空

本文求出零质量标量场产生的平面对称度规的静态通解,并研究了它的对称性、奇异性等整体特性,发现平面对称情况与球对称不同,标量场的引入与否,其时空的奇异性没有本质差别。 关键词：     

Tachyon Cosmology with Gauss–Bonnet and Non-Minimal Kinetic Couplings

We consider a tachyonic model of dark energy in which scalar field non-minimally coupled with curvature and kinetic part of its Lagrangian density.Additionally the model contains the Gauss–Bonnet coupling to the scalar field through an arbitrary function.The non-minimal Gauss–Bonnet coupling function and scalar field potential have been obtained for power-law solution and then for a dynamically varying equation of state.We have extracted the required condition for the so-called phantom divide line crossing in the model and represented such a crossing numerically.     

The soliton in the asymmetric scalar field theory

A new soliton solution for the asymmetric scalar field theory is obtained. The soliton is interpreted as the boson condensate drop. The phase transition is examined.     

Anisotropic power-law inflation of the five dimensional scalar–vector and scalar-Kalb–Ramond model

We will study the cosmological implications of the five dimensional scalar–vector and scalar-Kalb–Ramond model. In particular, a new set of Bianchi type I power-law analytic solution will be obtained for this model. The cosmic no-hair conjecture can be shown to break down in the presence of the scalar–vector and scalar-Kalb–Ramond couplings. The effect of the Kalb–Ramond field in the presence of the power-law solution will be shown explicitly. We will also show that the presence of a phantom field does, however, destabilize the corresponding Bianchi type I power-law inflationary solutions.     

Evolution of the Fermi surface of cuprates on the basis of the spin-polaron approach

A classical field system is considered that consists of two interacting scalar fields, the Higgs real field and a complex scalar field. It is demonstrated that there exists a nontrivial topological solution in this system—a kink carrying a U(1) charge. Certain questions are discussed related to the stability of the solution obtained. An improved variational procedure is proposed for determining topological U(1)-charged configurations.     

Scalar resonant frequencies and Hawking effect of an f(R) global monopole

Massive scalar fields are considered in the gravitational field produced by a Schwarzschild black hole with a global monopole in f(R) gravity.The exact solution of the radial part of the Klein-Gordon equation in this background is obtained and is given in terms of the general Heun functions.We apply the properties of the general Heun functions to study the Hawking radiation and the resonant frequencies of scalar particles.     

Gravitational stability of a massless scalar field

A solution is obtained to the Einstein equations for a static, spherically symmetric, massless scalar field. The stability of a static, massless scalar field for a point source is studied. It is found that the field is unstable for small ratios of the scalar charge of the source to its mass but is stable for large ratios. It is proven that there exists a dimensionless number which limits the region of stability for the field.Translated from Izvestiya Vysshikh Uchebnyk Zavedenii, Fizika, No. 7, pp. 79–83.     

Accuracy of scalar approximation for single-mode fibers

Total dispersion in single-mode fibers has been computed from the exact numerical solution of scalar and vector wave equations and the accuracy of the scalar approximation has been discussed. It has been shown that for larger values of relative index difference between core and cladding, although the values of total dispersion obtained by the two approaches differ appreciably in the vicinity of zero dispersion, the optimum core radii and the zero dispersion wavelengths obtained by the two methods differ negligibly for all practical purposes.     

Field of a Point Source Within Perfectly Conducting Parallel-Plates in a Homogeneous Biisotropic Medium

The spherical wave scattering response by a perfectly conducting open–ended waveguide in a biisotropic medium is obtained. Interestingly, the vector diffraction problem is reduced to the scattering of a single scalar field, this scalar field being the normal component of either a left–handed or a right–handed Beltrami field. Here, we explicitly consider the scattering of the left–handed field component, that of the other scalar field being analogously tractable. The solution is constructed with the aid of the Wiener–Hopf technique.     

Einstein场方程的一个平面对称非静态标量场解

求出一个特殊的标量场V=V(t-z)产生的平面对称度规的一个非静态解,并研究了它的对称性、奇异性等整体特性。 关键词：     

Anomalous behavior of a scalar particle in a globally regular space-time of a Schwarzschild black hole

The curved space-time Klein-Gordon equation in a globally regular space-time of a Schwarzschild black hole is solved, and its exact solution is obtained. The wave functions of a scalar particle inside the black hole are discussed by means of numerical analysis. The anomalous behaviors of the scalar particle in the central region of the black hole and in the interior neighborhood of the Schwarzschild event horizon are studied with the help of approximate solutions, which are compared with the exact one in these two regions.     

A scalar polynomial singularity without an event horizon

It is shown that the solution of the field equations for a static spherically symmetric scalar field has a scalar polynomial singularity and no event horizon. The solution does not develop from nonsingular data on any Cauchy surface. The possible existence of a universal scalar field, the conformal diagram and geodesies of the solution, and the energy and momentum of the field present are discussed.