Bianchi type V perfect-fluid space-times

A method is presented to generate exact solutions of the Einstein field equations in Bianchi type V space-times. The energy-momentum tensor is of perfect fluid type. Starting from particular solutions, new classes of solutions are obtained. The geometrical and physical properties of a class of solutions are discussed.     

A Systematic Method' for Constructing Solutions to the Yang-Baxter Equation

In this paper a systematic method, based on Jimbo's theorem, for constructing the spectrumdependent trigonometric solutions, as well aa the rational ones, to the Yang-Baxter equation is presented. Some solutions obtained by this method are discussed. The link polynomials constructed from the trigonometric solutions are obtained.     

Some new radiating Kerr-Newman solutions

Three exact non-static solutions of Einstein-Maxwell equations corresponding to a field of flowing null radiation plus an electromagnetic field are presented. These solutions are non-static generalizations of the well known Kerr-Newman solution. The current vector is null in all the three solutions. These solutions are the electromagnetic generalizations of the three generalized radiating Kerr solutions discussed by Vaidya and Patel. The solutions discussed by us describe the exterior gravitational fields of rotating radiating charged bodies. Many known solutions are derived as particular cases.     

Anisotropic fluid spheres in general relativity

A procedure is developed to find static solutions for anisotropic fluid spheres from known static solutions for perfect fluid spheres. The method is used to obtain four exact analytical solutions of Einstein’s equations for spherically symmetric self-gravitating distribution of anisotropic matter. The solutions are matched to the Schwarzschild exterior metric. The physical features of one of the solutions are briefly discussed. Many previously known perfect fluid solutions are derived as particular cases.     

LRS Bianchi type I perfect fluid solutions generated from known solutions

Some LRS Bianchi type I perfect fluid solutions are generated from known solutions of this type. The solutions represent spatially homogeneous and anisotropic cosmological models which would give essentially empty space for large time. The physical and kinematic properties of the models are discussed.     

The Fermi gas model of one-dimensional conductors

The Fermi gas model of one-dimensional conductors is reviewed. The exact solutions known for particular values of the coupling constants in a single chain problem (Tomonaga model, Luther-Emery model) are discussed. Renormalization group arguments are used to extend these solutions to arbitrary values of the couplings. The instabilities and possible ground states are studied by investigating the behaviour of the response functions. The relationship between this model and others is discussed and is used to obtain further information about the behaviour of the system. The model is generalized to a set of coupled chains to describe quasi-one-dimensional systems. The crossover from one-dimensional to three-dimensional behaviour and the type of ordering are discussed.     

Classical solutions to topologically massive Yang-Mills theory

Classical solutions to (2 + 1)-dimensional Yang-Mills theory in the presence of the Chern-Simons invariant are considered. The SO(3)-invariant solutions to the Euclidean field equations are complex, whereas the equations in Minkowski space-time possess real SO(2, 1)-invariant solutions. The field equations for time independent axially symmetric vector potentials are derived and some solutions are obtained. The behavior of general Euclidean spacetime solutions is discussed. It is also shown that, because of the gauge dependence of the Chern-Simons invariant, the reduced field equations cannot be uniquely obtained from the reduced action. Applications of the results to the infrared structure of finite temperature QCD are discussed; in particular, it is argued that the Chern-Simons invariant cannot be consistently incorporated as a gauge-invariant magnetic mass term in a three-dimensional effective long distance theory at high temperatures.     

Double-dual solutions of generalized theories of gravitation

Solutions to the Stephenson-Yang theory of gravity and its generalizations are discussed. By considering the inclusion of a cosmological term in the action spherically symmetric static solutions are presented that do not fall into the vacuum Einstein class. A simple double-duality ansatz is responsible for all the solutions that are discussed.On leave from the Physics Department, Middle East Technical University, Ankara, Turkey.     

Analytical solution of transverse oscillation in cyclotron using LP method

We have carried out an approximate analytical solution to precisely consider the influence of magnetic field on the transverse oscillation of particles in a cyclotron.The differential equations of transverse oscillation are solved from the Lindstedt-Poincare method.After careful deduction,accurate first-order analytic solutions are obtained.The analytical solutions are applied to the magnetic field from an isochronous cyclotron with four spiral sectors.The accuracy of these analytical solutions is verified and confirmed from comparison with a numerical method.Finally,we discussed the transverse oscillation at v_0=N/2,using the same analytical solution.     

Yang-Mills cosmologies and collapsing gravitational sphalerons

Cosmological solutions with a homogeneous Yang-Mills field which oscillates and passes between topologically distinct vacua are discussed. These solutions are used to model the collapsing Bartnik-McKinnon gravitational sphaleron and the associated anomalous production of fermions. The Dirac equation is analyzed in these backgrounds. It is shown explicity that a fermion energy level crosses from the negative to positive energy spectrum as the gauge field evolves between the topologically distinct vacua. The cosmological solutions are also generalized to include an axion field.     

An interior solution for the gamma metric

Interior solutions for a static, axially symmetric family of solutions of Einstein's equations are described. The interior solutions correspond to spatially bound matter and are properly matched to an exterior vacuum solution. The family of solutions discussed include the Schwarzschild solution as a special case. A general method is exhibited for transforming any spherically symmetric interior solution to an interior for the other members of the family of solutions. The energy density remains positive for at least a finite range of the parameter that describes the family of solutions. Two solutions are explicitly exhibited. One is transformed from the constant density Schwarzschild interior solution and one from the Adler interior solution. The first solution would be expected to be unstable under adiabatic perturbations of the matter, the second would be expected to be stable.Supported in part by The National Science Foundation under Grant No. INT 782-5663.Supported in part by Consejo Nacional de Investigaciones Cientificas y Technologicas (CONICIT), Venezuela.     

Properties of exact solutions for a massive classical Yang-Mills field

Exact solutions for a massive Yang-Mills field are found and solutions of classical Wong equations and quantum Dirac equations are discussed for the field configurations obtained. A procedure for constructing constant fields is given and transition to solutions of the Yang-Mills equations in the case of a massless field is discussed.Translated from Izvestriya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 96–100, May, 1986.In conclusion, the authors express their gratitude to V. Ch. Zhukovskii and V. R. Khalilov for valuable remarks and discussions.     

Kundt solutions of Einstein's equations with one non-null Killing vector

The Kundt class of algebraically special solutions of Einstein's field equations, representing vacuum and electromagnetic null fields with one twisting, non-null Killing vector, is discussed. This generalizes the case with a hypersurface-orthogonal Killing vector field which is discussed by Kramer and Neugebauer [3]. The solutions are shown to be equivalent to the Hoenselaers (vacuum) and Hoenselaers-Skea (electromagnetic null) solutions, once some small corrections and the relevant coordinate transformations are made to the latter solutions.     

Stationary rotating string world models with a magnetic field

Following the techniques used by Letelier and Stachel some new physically relevant stationary solutions of string cosmology with magnetic field are presented. In these solutions, the flow vector of matter has non-zero rotation and the cosmological constant is taken to be non-zero. Previously known solutions are derived as particular cases from our class of solutions. Some string models with vanishing cosmological constant are also discussed.     

Tilted rotation of triaxial nuclei

The Tilted Axis Cranking theory is applied to the model of two particles coupled to a triaxial rotor. Comparing with the exact quantal solutions, the interpretation and quality of the mean field approximation is studied. Conditions are discussed when the axis of rotation lies inside or outside the principal planes of the triaxial density distribution. The planar solutions represent ΔI = 1 bands, whereas the aplanar solutions represent pairs of identical ΔI = 1 bands with the same parity. The two bands differ by the chirality of the principal axes with respect to the angular momentum vector. The transition from planar to chiral solutions is evident in both the quantal and the mean field calculations. Its physical origin is discussed.     

Contribution of the short-range order to the effects of heat treatment on Cu-Al solid solutions

The contributions from the short-range order to the heat of transition and to the density change are discussed for Cu-Al solid solutions; it is confirmed that the transitions in undeformed Cu-Al solid solutions cannot be explained in terms of the short-range order alone.     

The motion of black holes

The motion of axisymmetric non rotating black holes is discussed using the properties of Weyl solutions. It is shown that there are no such solutions representing more than one black hole or black holes and ordinary massive bodies apart from the exceptional case of a massive body which surrounds or partially surrounds a black hole. A new exact solution is obtained representing a black hole chased by a negative mass particle, both objects being uniformly accelerated and all solutions representing a single black hole tidally distorted by an external static, axisymmetric gravitational field are obtained.     

Dielectric polarization of the solutions of nitrotoluene and cyclohexane

Dielectric properties of the solutions of nitrotoluene in cyclohexane showing a far pre-critical state are discussed. Dipolar polarization of the solutions was calculated on the lines of the Onsager model of local field, while the energy of interdipolar interactions was calculated with the help of the dipole-dipole coupling model given by Piekara. The character of interdipolar interactions in the solutions studied was found to be analogous to those in critical solutions at the temperatures from 10 to 20 K higher than the critical temperature.     

A class of new LRS Bianchi type-I perfect fluid universes with decaying vacuum energy density Λ

A class of new LRS Bianchi type-I cosmological models with a variable cosmological term is investigated in presence of perfect fluid. A procedure to generate new exact solutions to Einstein’s field equations is applied to LRS Bianchi type-I space-time. Starting from some known solutions a class of new perfect fluid solutions of LRS Bianchi type-I are obtained. The cosmological constant Λ is found to be positive and a decreasing function of time which is supported by results from recent supernovae Ia observations. The physical and geometric properties of spatially homogeneous and anisotropic cosmological models are discussed.