On spherically symmetric singularity-free models in relativistic cosmology

The introduction of time dependence through a scale factor in a non-conformally flat static cosmological model whose spacetime can be embedded in a five demensional flat spacetime is shown to give rise to two spherical models of universe filled with perfect fluid acompannied with radial heat flux without any Big Bang type singularity. The first model describes an ever existing universe which witnesses a transition from state of contraction to that of ever expansion. The second model represents a universe oscillating between two regular states.     

Admissible coordinate systems for static,spherically symmetric stellar models

For static, spherically symmetric stellar models it is shown that imposing the condition that the determinant of the metrical coefficients takes on its flat space-time value everywhere is sufficient to ensure that the coordinates are admissible in the sense of Lichnerowicz. The general method of solution is illustrated by integrating the equations for a star of constant, uniform density.     

Expanding spherically symmetric models without shear

The integrability properties of the field equationL _xx =F(x)L ² of a spherically symmetric shear-free fluid are investigated. A first integral, subject to an integrability condition onF(x), is found, giving a new class of solutions which contains the solutions of Stephani and Srivastava as special cases. The integrability condition onF(x) is reduced to a quadrature which is expressible in terms of elliptic integrals in general. There are three classes of solution and in general the solution ofL _xx =F(x)L ² can only be written in parametric form. The case for whichF=F(x) can be explicitly given corresponds to the solution of Stephani. A Lie analysis ofL _xx =F(x)L ² is also performed. If a constant vanishes, then the solutions of Kustaanheimo and Qvist and of this paper are regained. For 0 we reduce the problem to a simpler, autonomous equation. The applicability of the Painlevé analysis is also briefly considered.     

General spherically symmetric elastic stars in relativity

The relativistic theory of elasticity is reviewed within the spherically symmetric context with a view towards the modeling of star interiors possessing elastic properties such as the ones expected in neutron stars. Emphasis is placed on generality in the main sections of the paper, and the results are then applied to specific examples. Along the way, a few general results for spacetimes admitting isometries are reviewed, and their consequences are fully exploited in the case of spherical symmetry relating them next to the the case in which the material content of the spacetime is some elastic material. Specific examples are provided satisfying the dominant energy condition and admitting a constitutive equation, including a static two-layer star ‘toy model’ consisting of an elastic core surrounded by a perfect fluid corresponding to the interior Schwarzschild solution matched to the vacuum Schwarzschild solution. This paper extends and generalizes the pioneering work by Magli and Kijowski (Gen Relat Gravit 24:139, 1992), Magli (Gen Relat Gravit 25:1277, 1993; 25:441, 1993), and complements, in a sense, that by Karlovini and Samuelsson in their interesting series of papers (Karlovini and Samuelsson in Class Quantum Grav 20:363, 2003; 21:1559, 21:4531, 2004).     

General solution of the spherically symmetric Yang-Mills equations

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

Radiation fields of multilayered spherically symmetric systems

The luminescence of spherical multilayered systems with a stationary radiation field in a continuum is considered. The formal solution of the transport equation is shown to be equivalent to the solution of the Cauchy problem for the set of characteristic functions. The differential equations and initial conditions for these functions are formulated and their properties are established.     

电磁波在径向非均匀球对称等离子体中的衰减

提出了一种计算任意入射角的电磁波在径向非均匀球对称等离子体中的传播和吸收的模型.在此模型中，把非均匀等离子体球分成若干个同心等离子体球壳，并且假定每一个同心壳层内等离子体密度均匀分布.采用几何光学近似方法，考虑相位系数和衰减系数的矢量性，分别研究了几种典型的非均匀密度分布形式的等离子体在不同碰撞频率、中心等离子体密度和电磁波入射角条件下对入射电磁波的传播和衰减特性，获得了一些有意义的结果. 关键词： 电磁波 碰撞频率 等离子体球 能量衰减     

On Datta's spherically symmetric systems in general relativity

The problem tackled by B. K. Datta, [1] in a recent paper concerning non-static spherically symmetric systems in which the particle motion is, in a certain sense, purely transverse, is further developed and compared with the Newtonian case. A full classification of the possible motions is given.The author wishes to express his thanks to Professor C. W. Kilmister for helpful discussions.     

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.     

General form for the longitudinal momentum of a spherically symmetric source

A simple form and its physical interpretation are presented for a solution of the momentum constraint in the initial-value problem of general relativity.     

Issue of the spherically symmetric static vacuum metric in the relativistic theory of gravity

The spherically symmetric vacuum metric in the relativistic theory of gravity is analyzed numerically. It is found that there is no deviation of the numerical solution from that of general relativity except in the near-horizon range. The solution obtained has the well-established analytical asymptotics for both the near-and far-horizon limits. It satisfies the causality principle and does not impose a lower limit on the graviton mass.      

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.     

Simple solutions of relativistic hydrodynamics for cylindrically symmetric systems

Simple, self-similar, analytic solutions of 1+3-dimensional relativistic hydrodynamics are presented for cylindrically symmetric fireballs corresponding to central collisions of heavy ions at relativistic bombarding energies.     

General relativistic dynamics of compact binary systems

The equations of motion of compact binary systems have been derived in the post-Newtonian (PN) approximation of general relativity. The current level of accuracy is 3.5PN order. The conservative part of the equations of motion (neglecting the radiation reaction damping terms) is deducible from a generalized Lagrangian in harmonic coordinates, or equivalently from an ordinary Hamiltonian in ADM coordinates. As an application, we investigate the problem of the dynamical stability of circular binary orbits against gravitational perturbations up to the 3PN order. We find that there is no innermost stable circular orbit or ISCO at the 3PN order for equal masses. To cite this article: L. Blanchet, C. R. Physique 8 (2007).     

A static spherically symmetric solution for interacting scalar,electromagnetic, and gravitational fields

A unified theory of interacting scalar, electromagnetic, and gravitational fields constructed in previous papers by the author is used in considering a static spherically symmetrical case. An effective one-dimensional Lagrangian is derived together with the corresponding Hamilton-Jacobi equation. The solution to this equation is used in deriving a solution to Einstein's equations for the initial system of interacting fields. Some consequences of the solution are examined. A relationship is derived between the constants of integration that ensures finiteness in the total field energy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 74–80, March, 1980.I am indebted to Yu. S. Vladimirov and V. N. Mel'nikov, as well as other participants in the seminar of the Gravitation Section of the Ministry of Technical Colleges of the USSR, for their interest and valuable comments.