General solution of the spherically symmetric Yang-Mills equations

A general solution of the spherically symmetric Yang-Mills equations is presented.     

A singularity free solution of the Maxwell-Einstein equations

It is found that the massless charged particle permanently at rest at the origin of spherical polar coordinates in Lovelock's interpretation [1] of Robinson's solution of the Einstein-Maxwell equations [2] will repel all charged test particles, irrespective of the sign of their charges. By a global embedding of the space-time in a flat 6-space we find an absence of singularities where point-charges or point-masses might be located. With the use of the Newman-Penrose method of spin-coefficients [6] it is shown that all the Robinson solutions [2] represent constant electromagnetic fields.     

A charged spherically symmetric solution

We find a solution of the Einstein-Maxwell system of field equations for a class of accelerating, expanding and shearing spherically symmetric metrics. This solution depends on a particularansatz for the line element. The radial behaviour of the solution is fully specified while the temporal behaviour is given in terms of a quadrature. By setting the charge contribution to zero we regain an (uncharged) perfect fluid solution found previously with the equation of statep = μ + constant, which is a generalisation of a stiff equation of state. Our class of charged shearing solutions is characterised geometrically by a conformal Killing vector.     

Numerical spherically symmetric static solution of the RTG equations outside of matter

There was obtained a numerical external solution for the exact system of the RTG equations using natural boundary conditions in the static spherically symmetric case. The properties of the solution are discussed.      

Vaidya's spherically symmetric radiating solution

Conclusions An analysis of Vaidya's solution has shown that it cannot describe electromagnetic radiation in a gravitational field: the Einstein-Maxwell equations for this solution are incompatible.The neutrino treatment of this solution is somewhat dubious.An investigation using the Rodichev energy tensor and Petrov's classification indicates that there is also no gravitational radiation in this solution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 130–132, November, 1971.In conclusion the authors wish to thank V. I. Rodichev for valuable discussions of this work.     

Static spherically symmetric solutions of the Einstein-Yang-Mills equations

We study the global behaviour of static, spherically symmetric solutions of the Einstein-Yang-Mills equations with gauge groupSU(2). Our analysis results in three disjoint classes of solutions with a regular origin or a horizon. The 3-spaces (t=const.) of the first, generic class are compact and singular. The second class consists of an infinite family of globally regular, resp. black hole solutions. The third type is an oscillating solution, which although regular is not asymptotically flat.This article was processed by the author using the Springer-Verlag TEX CoMaPhy macro package 1991.     

Non-integrability of time-dependent spherically symmetric Yang-Mills equations

The integrability of time-dependent spherically symmetric Yang-Mills equations is studied using the Fermi-Pasta-Ulam method. It is shown that the motion of this system is ergodic, while the system itself is non-integrable, i.e. manifests dynamical chaos.     

Static spherically symmetric solutions of the classical Yang-Mills equations

All spherically symmetric solutions with time-independent fields are found for the classical Yang-Mills equations with an extended charge in the case of the SU(2) gauge group. There is a physically different solution corresponding to each choice of an arbitrary function of radius. In all solutions the energy and the charge are reduced compared to the Coulomb solution. For certain solutions the reduced charge and all fields outside the source vanish.     

Charged spherically symmetric solution in Mikhail-Wanas field theory

A set of coupled differential equations obtained by Wanas in the Mikhail-Wanas generalized field theory is completely integrated.     

Generation and construction of statistical spherically symmetric solutions of the gravitational equations

We show that the possibility of reducing the Einstein equations in isotropic Bondi coordinates for a spherically symmetric statistical case to two forms of a linear differential equation allows one to introduce procedures for generating a fortiori exact solutions of the gravitational equations from the known ones. A superposition of solutions is defined in a special way. Examples are given of the known solutions obtained in this way from flat space-time. The use of the proposed generating procedures allows one to find all exact solutions of the gravitational equations for neutral sources in the statistical, spherically symmetric case.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 5–9, June, 1990.     

A general integral of the Jordan-Brans-Dicke field equations for static spherically symmetric perfect fluid distributions

The Jordan-Brans-Dicke field equations [1] contain the four-dimensional field equations of the five-dimensional projective unified theory. As it should be, Einstein's theory is incorporated as a limiting case. In this paper we present a method to determine explicitly for every static spherically symmetric solution of Einstein's theory with perfect fluid an analogous solution of Jordan-Brans-Dicke theory. As a particular example a “generalized interior Schwarzschild solution” is given.     

A special exact spherically symmetric solution in f(T) gravity theories

A non-diagonal spherically symmetric tetrad field, involving four unknown functions of radial coordinate $r$ r , is applied to the equations of motion of f(T) gravity theory. A special exact vacuum solution with one constant of integration is obtained. The scalar torsion related to this special solution vanishes. To understand the physical meaning of the constant of integration we calculate the energy associated with this solution and show how it is related to the gravitational mass of the system.     

Numerical solution of the radiative transfer equation in spherically symmetric dust shells

An efficient numerical method is presented for solving problems of radiative transfer in dust shells with spherical symmetry. The method can be applied to a wide variety of radiative transfer problems in planetary atmospheres, circumstellar dust envelopes and extended stellar atmospheres. The computational procedure and practical considerations for implementing the method are described in detail. As an illustration, the method is used to determine the grain temperature distribution and far i.r. emission from interstellar dust clouds associated with compact HII regions. Generalizations to problems involving cylindrical geometry and multi-temperature dust shells are discussed in the appendices.     

Force multipole moments for a spherically symmetric particle in solution

We present a general theorem for the force multipole moments of arbitrary order induced in a spherically symmetric particle immersed in a fluid whose motion satisfies the linear Navier-Stokes equation for steady incompressible viscous flow. The multipole moments are expressed in terms of the unperturbed fluid velocity field. It is shown that for a particle with a finite extension only a few terms give rise to fluid perturbations which are not confined to the interior of the particle. We give explicit results for a polymer satisfying the Debye-Bueche-Brinkman equations and for a hard sphere with mixed slip-stick boundary conditions.     

Singularities in solutions of the Einstein equations for a static spherically symmetric field

Russian Physics Journal - The nature of the singularities in the solutions of Einstein's equations for a static spherically symmetric field is investigated as a function of the choice of...     

Particle motion in the spherically symmetric vacuum solution with positive cosmological constant

The time-like geodesics in the spherically symmetric vacuum solution with positive cosmological constant are investigated. The conditions necessary for the existence of bound orbits are found and the motion of particles is related to their position in the conformal diagram.     

The general class of the vacuum spherically symmetric equations of the general relativity theory

The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g ₀₀ and g ₂₂ is obtained. The properties of the found solutions are analyzed.