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.     

On the dynamics of a thin spherically symmetric radiating shell,its classical model,and relativistic effects

A general relativity model of nova and supernova explosions is studied and improved. Its classical limit is found, and the magnitude of the velocity and mass necessary to detect relativistic effects are computed.     

External gravitational field of a non-static spherically symmetric body

It is shown that in the field theory of gravitation, the external gravitational field of a non-static spherically symmetric source described by a diagonal metric tensor can be static only.     

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.     

Static spherically symmetric anisotropic fluid distribution in presence of electromagnetic field

Einstein’s field equations of general relativity corresponding to the anisotropic (principal stresses unequal) static fluid sphere in presence of electromagnetic field have been solved exactly. The integration constants are determined by matching the obtained solution with the Reissner-Nordström solution over the boundary. It has been found that the flaid model has non-negative expression for mass density and pressure. The mass density and stresses are everywhere regular and monotonically decreasing functions of the radial coordinate.     

The character of an anisotropic and spherically symmetric star in the presence of a cosmological constant

From the gravitational structure equations of an anisotropic and spherically symmetric star in the presence of a cosmological constant, we derive the inequality which limits the mass-radius ratio, imposing energy conditions on the matter, From this inequality, we display how the cosmological constant modifies the Buchdahl limit, and express the bounds on both the mass-radius ratio and surface redshiR in terms of the ratio between the cosmological constant and mean energy density of the star.     

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 gravitational collapse-field with radiation

An interior spherically symmetric solution of Einstein’s field equations corresponding to perfect fluid plus a flowing radiation-field is presented. The physical 3-spacet=constant of our solution is spheroidal. Vaidya’s pure radiation field is taken as the exterior solution. The inward motion of the collapsing boundary surface follows from the equations of fit. An approximation procedure is used to get a generalization of the standard Oppenheimer-Snyder model of collapse with outflow of radiation. One such explicit solution has been given correct to second power of eccentricity of the spheroidal 3-space.     

Radiation transport in a spherically symmetric hot plasma

An analytical solution is obtained for the problem of radiation transport in a spherically symmetric plasma. The ions are assumed to be in a complete steady state with constant ion density and electron temperature. The radiation density is assumed to be small so that the rate of the radiative processes in the plasma is small relative to that of the collisional processes, but not negligible. The effect of the plasma on the radiation density, as well as the influence of the radiation on the population probabilities, are properly accounted for. Under these conditions explicit expressions are given, valid to the first order in the plasma dimensions, for the radiation density and the population probability of the ionic states.     

A class of spherically symmetric ideal fluid fields

It is shown that the equation of state =p for an ideal fluid follows from the condition of integrability of Einstein's equations for the metric ds²=R²T²d²+e²dr²–e²dt². In this case, the system of Einstein's equations turns out to be indeterminate and has an infinite number of solutions for R 0. These solutions describe fields with nonzero acceleration, expansion, and shear tensor of particles. The obtained solutions correct the results obtained by J. Hajj-Boutros, J. Math. Phys.,26, 771 (1985). The unique solution of Einstein's equations for the state =p of a fluid is obtained to within arbitrary constants for R=0.Naval Engineering College, Novosibirsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 91–94, June, 1992.     

Geometric inequalities in spherically symmetric spacetimes

In geometric inequalities ADM mass plays more fundamental role than the concept of quasi-local mass. This paper is to demonstrate that using the quasi-local mass some new insights can be acquired. In spherically symmetric spacetimes the Misner–Sharp mass and the concept of the Kodama vector field provides an ideal setting to the investigations of geometric inequalities. We applying the proposed new techniques to investigate the spacetimes containing black hole or cosmological horizons but we shall also apply them in context of normal bodies. Most of the previous investigations applied only the quasi-local charges and the area. Our main point is to include the quasi-local mass in the corresponding geometrical inequalities. This way we recover some known relations but new inequalities are also derived.     

On the spherically symmetric gauge fields

The spherically symmetric gauge fields with a compact gauge group over 4-dimensional Minkowski space are determined completely. Expressions for the gauge potentials of these fields are obtained.     

Escape factors in spherically symmetric plasmas

In this paper we present explicit formulas for the escape factors of strong spectral lines in spherical-symmetric plasmas. The plasma does not necessarily have a homogeneous density. The calculations include two new elements: the first incorporates an accurate calculation of the angle-averaged areal density of ions from any internal point to the edge of the sphere. The second is the use of a saddle point method to carry out the integration over the line profile. Approximate expressions for the asymptotic behavior of the escape factor are given for Gaussian, Lorentzian and Holtsmarkian line shapes.     

Relativistic fluids in spherically symmetric space

Some of McVittie and Wiltshire's (1977) solutions of Walker's (1935) isotropy conditions for relativistic perfect-fluid spheres are generalized. Solutions are spherically symmetric and conformally flat.     

Static spherically symmetric anisotropic fluid distribution in presence of electromagnetic field in the Sen-Dunn theory of gravitation

Acta Physica Hungarica A) Heavy Ion Physics - In this paper a solution corresponding to a static spherically symmetric anisotropic fluid distribution in presence of electromagnetic field is...     

The dynamics of a thin spherically-symmetric radiating shell

The conclusions of paper [2] are modified: using the shell formalism, relativistic effect could eventually be detected in X-ray bursters.     

Self-consistent spherically symmetric solutions of the Yang-Mills-Dirac-equations

TheSU(2) Yang-Mills equations coupled self-consistently to an isospin 1/2-Dirac equation are studied. Static spherically symmetric exact analytic solutions are given. They all share the property of infinite energy.     

Static spherically symmetric fields in the scalar-tetradic theoryA

The scalar-tetradic TheoryA has been recently formulated. In this paper it is proved that, for a suitable tetrad field and any given value of the coupling constantW of the theory, there is a unique static spherically symmetric solution of the field equations describing the outer field of a standard perfect fluid sphere (such as the sun); the explicit form of this solution in terms of the radial isotropic coordinater appears to be different in the three cases: (1)W <0 orW > 2, (2) 0 <W < 2, and (3)W =2. On account of the Birkhoff theorem the quoted solution appears to have considerable physical interest.