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.     

Cascade evolution of spherically symmetric pulsons in multivacuum field theory models

Spherically symmetric oscillating solitons of a new type have been observed; their stability and instability regions have been found to be defined by the “potential relief” structure.     

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.     

Charged axially symmetric solution and energy in teleparallel theory equivalent to general relativity

An exact charged solution with axial symmetry is obtained in the teleparallel equivalent of general relativity. The associated metric has the structure function G(ξ)=1-ξ²-2mAξ³-q²A²ξ⁴. The fourth order nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad whose metric has the structure function in a factorizable form (1-ξ²)(1+r₊Aξ)(1+r_-Aξ) with r_± as the horizons of Reissner–Nordström space-time. This new form has the advantage that its roots are now trivial to write down. Then, we study the singularities of this space-time. Using another coordinate transformation, we obtain a tetrad field. Its associated metric yields the Reissner–Nordström black hole. In calculating the energy content of this tetrad field using the gravitational energy-momentum, we find that the resulting form depends on the radial coordinate! Using the regularized expression of the gravitational energy-momentum in the teleparallel equivalent of general relativity we get a consistent value for the energy.     

A scalar Euclidean theory of gravitation: motion in a static spherically symmetric field

The motion of a particle in a static, spherically symmetric gravitational field is investigated in Euclidean space. The gravitational effects are described as due to a scalar field: To every point in space there is assigned a refractive index deciding the velocity of light in that point. The motion of light in the vacuum is described by the equation of classical optics. An equation of motion for material test particles is then derived by employing the usual Lagrangian formalism. The motion of the planets around the sun is explained, in particular the perihelion motion of Mercury. The present theory fully explains the four classical tests of general relativity in a mathematically far simpler way, and it can be equivalent to the Schwarzschild solution. It is also found that the effect of gravitation depends on the velocity of the particle, becoming repulsive for radial velocities larger thanc/ (c is the velocity of light). This seemingly odd result can also be obtained from the equations of general relativity, as was shown by Cavalleri and Spinelli.     

Exact solutions for the spherically symmetric vacuum field in the general scalar tensor theory

A conformai technique is given for the generation of exact solutions for the spherically symmetric vacuum field in the general Bergmann-Wagoner-Nordtvedt scalar-tensory theory with vanishing cosmological constant. We discuss in particular the solution for Schwinger's theory and for models with ⁿ coupling or with curvature coupling. It appears that all theories with vanishing cosmological term lead to the presence of naked singularities.     

General solution of the spherically symmetric Yang-Mills equations

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

A spherically symmetric solution of the Maxwell-Einstein equations

A spherically symmetric solution of the already unified field theory ofRainich (i.e. of the source-free Maxwell-Einstein equations) is presented which represents a static massless charged particle. It is not equivalent to the Reissner-Nordström solution with zero mass, although both metrics repel uncharged test particles.On leave of absence from the Department of Mathematics, The University, Bristol.     

A spherically symmetric vacuum solution of the quadratic Poincaré gauge field theory of gravitation with newtonian and confinement potentials

We derive a stationary spherically symmetric vacuum solution in the framework of the Poincaré gauge field theory with a recently proposed quadratic lagrangian. We find a metric of the Schwarzschild-de Sitter type, both torsion and curvature are non vanishing, with torsion proportional to the mass and curvature proportional to the strong coupling constant κ. The metric exhibits two pieces, a newtonian potential describing the gravitational behavior of macroscopic matter, and a confining potential ～κr² presumably related to the strong-interaction properties of hadrons. To our knowledge this is a new feature of a classical solution of a Yang-Mills type gauge theory.     

Nonstatic spherically symmetric space-times in Rosen's bimetric gravitation theory

Time dependent metrics, conformally equivalent to the static spherically symmetric metric, are considered. The one-body problem is investigated and some general conditions for accelerated and geometrically modified orbiting are obtained. The radial and nonradial null geodesics are investigated and it is shown that their differential equations are not modified by the conformal factor.     

The gravitational field of static spherically symmetric bodies

The study of a previously proposed theory of gravitation [Petry, W. (1979).Gen. Rel. Grav.,10, 599; (1981).Ibid,13, 865] is continued. The field equations are given in a simple covariant form. For a perfect fluid with pressure the static spherically symmetric solutions of the gravitation theory are studied. Inertial and gravitational mass are identical. The solutions agree with the corresponding results of the theory of general relativity up to high order in the coupling constant. Under some natural conditions the solutions of a static spherically symmetric body are not singular.     

Neutrino oscillations in the general spherically symmetric gravitational field

The results for neutrino oscillations in the gravitational field described by the Schwarzschild metric are generalized to the general spherically symmetric gravitational field.     

The gravitational field of spherically symmetric matter distributions in the Yang-Mills gauge theory of gravity

In the new SO(1,3)-gauge theory of gravity, the exterior gravitational field of any spherically symmetric equilibrium distribution of matter and non-gravitational force fields is determined by two parameters, the gravitational mass M and the structure parameter γ. We discuss the physical interpretation of the parametrized post-Newtonian parameter γ in this theory of gravity. The boundary conditions fix uniquely the values of M and γ; it turns out that γ ? 1 is a measure for the gravitational binding of the source. In the Newtonian limit, stars with negligible radiation pressure are characterized by $\text{γ=1?}\text{2}\text{3}\text{M}\text{R}$, while radiation-dominated stellar structures may even have γ > 1; the value of γ for tightly bound neutron stars of one solar mass is about 0.9.     

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.     

Point charge in a static,spherically symmetric Brans-Dicke field

We determine in closed form the electrostatic potential of a point test charge held at rest in a static, spherically symmetric Brans-Dicke field. This result is a generalization of the previously obtained expression for the potential of a test charge at rest near a Schwarzschild black hole. Moreover, our solution is valid for the coupled gravitational and massless scalar fields.