Plane Symmetric Inhomogeneous Cosmological Models with a Perfect Fluid in General Relativity

In this paper we investigate a class of solutions of Einstein equations for the plane- symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three classes of solutions. PACS No.: 04.20.-q.     

Plane Symmetric String Cosmological Model in Modified Theory of General Relativity

It is shown that homogeneous plane symmetric string cosmological model for Takabayasi string i.e. ρ=(1+ω)λ does not exist in Barber’s second self creation theory. Further it is found that the string cosmological model in this theory exist only when ω=0. Therefore model for ρ=λ (geometric string) is constructed. Some physical and geometrical properties of the model are discussed.     

Perturbative Solutions of the Extended Constraint Equations in General Relativity

The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface in an asymptotically simple space-time satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on , and are equivalent to the usual constraint equations that satisfies as a space-like hypersurface in a space-time satisfying Einstein’s vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the ‘classical’ method of Lichnerowicz and York that is used to solve the usual constraint equations.     

Field Equations due to a Constant Modification in General Relativity

In this article, by adding a constant to Einstein-Hilbert action, we derive field equations for a non-vacuum space. Also we derive a general solution for these field equations, considering a de Sitter like initial geometric constraint. It is shown that how this additional constant can affect usual gravitational field equations, which are derived from general relativity.     

Plane Symmetric Solutions in f(R,T) Gravity

The main purpose of this paper is to investigate the exact solutions of plane symmetric spacetime in the context of f(R,T)gravity[Phys.Rev.D 84(2011)024020],where f(R,T)is an arbitrary function of Ricci scalar R and trace of the energy momentum tensor T.We explore the exact solutions for two different classes of f(R,T)models.The first class f(R,T)=R+2f(T)yields a solution which corresponds to Taub's metric while the second class f(R,T)=f_1(R)+f_2(T)provides two additional solutions which include the well known anti-deSitter spacetime.The energy densities and corresponding functions for f(R,T)models are evaluated in each case.     

A Note on Plane Symmetric Solutions in f(R) Gravity

The static plane symmetric vacuum solutions (Sharif and Shamir in Mod. Phys. Lett. A 25:1281, 2010) for n+1 dimension are reported. For this purpose, the generalized field equations are solved using the assumption of constant scalar curvature in metric f(R) gravity.     

Exact Solutions for Shear-free Motion of Spherically Symmetric Charged Perfect Fluid Distributions in General Relativity

An in-depth study of various methods, and their correlations, of obtaining exact solutions of Einstein-Maxwell field equations representing shear free motion of spherically symmetric charged perfect fluid distributions has been made. It is shown that one can employ isotropic coordinate systems without any loss of generality. However the investigations have been carried out in an arbitrary coordinate system. The exact solutions relating to simple situations viz. (i) homogeneous density distribution, ϱ=ϱ(t), (ii) conformally flat solutions and (iii) distributions obeying an equation of state, p=p(ϱ) are briefly discussed. The methods due to MCVITTIE (1967), introduced initially for neutral fluids, and MASHHON and PARTOVI (1979) where one assumes the metric in a convenient form form one group and the methods due to SHAH and VAIDYA (1968), CHAKRAVARTY and CHATTERJEE (1978), CHATTERJEE (1984) and SUSSMAN (1987) where one chooses suitably two arbitrary functions of integration form the other group. This splitting of various methods into two is based on the earlier analogous work for the neutral fluids due to SRIVASTAVA (1987). Using McVittie's procedure we obtain a solution which in its uncharged limit reduces to Friedmann-Robertson-Walker solution whereas for non-vanishing charge is equivalent to the solution due to SHAH and VAIDYA (1967). This solution is termed as generalised Shah-Vaidya solution or charged Friedmann-Robertson-Walker solution. A suitable generalisation of Mashhoon and Partovi's procedure has been found to contain MASHHOON-PARTOVI solution (1979) and SHAH-VAIDYA solution (1967) as members of a class. The method employed by CHATTERJEE (1978), which does not yield the general solution of the problem, has been shown to lead to the procedure adopted by SUSSMAN (1987) after it is generalised suitably. The McVittie type and Wyman type solutions introduced by Sussman has been found to be contained in McV class of metries discussed here. It is also found that solutions obtained by CHAKRAVARTY and CHATTERJEE (1978) represent a class of charged Kustaanheimo-Qvist solution which are expressible as elementary functions. Finally, all known solutions have been derived introducing an adhoc assumption in the form of a mathematical relation and searching for the solutions free from movable critical points.     

Solutions of the Field Equations and Possible Meaning of the Hermitian Theory of Relativity

A procedure is stated, which allows to build solutions of the Hermitian theory of relativity from known solutions of the general theory of relativity. Solutions depending on three co-ordinates, built from Minkowski metric, as well as Hermitian generalizations of the Weyl-Levi Civita solution are shown. They suggest that the imaginary part of the fundamental tensor may encompass fields of different physical behaviour, like the electromagnetic field and a field responsible for forces which do not depend on the distance between charges which cannot exist as individuals. In the generalizations of the Weyl-Levi Civita solution these fields appear to be decoupled from gravitation in a peculiar way.     

Exact Solitary Wave Solutions of the Coupled Nonlinear Scalar Field Equations

Because of the arbitrary property of the singular manifold, the usual singularity analysis can be extended to a different form. Using a nonstandard truncation approach, five special types of exact solution of the coupled nonlinear scalar field equations are obtained.     

Wave Fronts for Hamilton-Jacobi Equations:¶The General Theory for Riemann Solutions in

The Hamilton-Jacobi equation describes the dynamics of a hypersurface in . This equation is a nonlinear conservation law and thus has discontinuous solutions. The dependent variable is a surface gradient and the discontinuity is a surface cusp. Here we investigate the intersection of cusp hypersurfaces. These intersections define (n-1)-dimensional Riemann problems for the Hamilton-Jacobi equation. We propose the class of Hamilton-Jacobi equations as a natural higher-dimensional generalization of scalar equations which allow a satisfactory theory of higher-dimensional Riemann problems. The fist main result of this paper is a general framwork for the study of higher-dimensional Riemann problems for Hamilton-Jacobi equations. The purpose of the framwork ist to unterstand the structure of Hamilton-Jacobi wave interactions in an explicit and constructive manner. Specialized to two-dimensional Riemann problems (i.e., the intersection of cusp curves on surfaces embedded in ), this framework provides explicit solutions to a number of cases of interest. We are specifically interested in models of deposition and etching, important processes for the manufacture of semiconductor chips. We also define elementary waves as Riemann solutions which possess a common group velocity. Our second main result, for elementary waves, is a complete characterization in terms of algebraic constraints on the data. When satisfied, these constraints allow a consistently defined closed form expression for the solution. We also give a computable characterization for the admissibility of an elementary wave which is inductive in the codimension of the wave, and which generalizes the classical Oleinik condition for scalar conservation laws in one dimension. Received: 9 September 1996 / Accepted: 22 April 1997     

Non-Vacuum Plane Symmetric Solutions and their Energy Contents in f (R) Gravity

The exact vacuum solutions of static plane symmetric spacetimes in four, five, six and n-dimensions in metric approach of f (R) theory of gravity have already been found and are available in literature. In this paper, we extend the work done by Sharif and Farasat for the case of vacuum static plane symmetric solutions in f (R) theory of gravity to non-vacuum case. Two non-vacuum solutions have been determined by using constant Ricci scalar assumption. Moreover, for some specific choices of f (R) models, the energy distribution of these solutions has been explored by applying the generalized Landau-Lifshitz energy-momentum complex in the context of f (R) theory of gravity. In addition, we discuss the stability conditions for these solutions.     

Vacuum Birefringence in a Field of a Plane Electromagnetic Wave

Optics and Spectroscopy - The process of vacuum birefringence in a strong electromagnetic field is investigated, in which a probe photon changes its polarization when passing through a...     

Electrodynamics of a Scalar Particle in a Plane Electromagnetic Wave Field

In the present paper, compact expressions are derived for the probability of photon emission by a scalar particle and for the probability of creating pairs of scalar particles in an arbitrary plane electromagnetic wave field. Based on these general expressions, the amplitude of elastic scattering of a scalar particle and the amplitude of elastic scattering of a photon are derived by the method of dispersion relations (in the first-order approximation for the fine-structure constant ₀ = e ²/4). The real components of these amplitudes determine the radiative corrections for particle masses in the examined fields. Some particular cases of the plane wave field are examined. In particular, the above-indicated amplitudes in the external electromagnetic field being a superposition of a constant crossed field and a plane elliptically polarized electromagnetic wave propagating along the direction orthogonal to the magnetic and electric components of the constant crossed field are investigated. The amplitude of elastic scattering of a scalar particle in an arbitrary plane electromagnetic wave field is also obtained by direct calculations of the corresponding mass operator of the scalar particle in this field.     

Identification of excited states in the T(z) = 1 nucleus (110)Xe: evidence for enhanced collectivity near the N=Z=50 double shell closure

Gamma-ray transitions have been identified for the first time in the extremely neutron-deficient (N=Z+2) nucleus (110)Xe, and the energies of the three lowest excited states in the ground-state band have been deduced. The results establish a breaking of the normal trend of increasing first excited 2(+) and 4(+) level energies as a function of the decreasing neutron number as the N=50 major shell gap is approached for the neutron-deficient Xe isotopes. This unusual feature is suggested to be an effect of enhanced collectivity, possibly arising from isoscalar n-p interactions becoming increasingly important close to the N=Z line.