Further remark concerning spherically symmetric nonstatic separable solutions to the Einstein equations in the comoving frame

We consider nonstatic spherically symmetric fluid solutions to the Einstein equations which, in the comoving frame, have metric coefficients that are separable functions of their arguments and that have an origin. Subject to the vanishing of the heat flux, we show that all such solutions with shear and non-vanishing shear viscosity have a scalar polynomial singularity at the origin if the fluid satisfies both the weak and strong energy conditions. When combined with previous results [1] we conclude that for the metric forms under consideration, the only fluid solutions to the Einstein equations with vanishing heat flux which satisfy the energy conditions and are free of singularities at the origin are the Robertson-Walker solutions.     

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...     

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.     

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.     

Hawking thermal radiation of the dirac particle in spherically symmetric nonstatic space-time

The dynamical properties of Dirac spinor particles in a spherically symmetric nonstatic space-time are studied. The explicit representative of the four-component wave function of Dirac particles is obtained. The Dirac equation can be reduced to the standard form of the wave equation near the event horizon by the proper coordinate transformation. The event horizon location and Hawking radiation temperature are obtained.     

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.     

Global existence of generalized solutions of the spherically symmetric Einstein-scalar equations in the large

In this paper we study the global initial value problem for the spherically symmetric Einstein-scalar field equations in the large. We introduce the concept of a generalized solution of our problem, and, taking as initial hypersurface a future light cone with vertex at the center of symmetry, we prove, without any restriction on the size of the initial data, the global, in retarded time, existence of generalized solutions.Research supported in part by National Science Foundation grants MCS-8201599 to the Courant Institute and PHY-8318350 to Syracuse University     

Spherically symmetric nonstatic perfect fluid solutions with shear

In this paper we investigate solutions of Einstein's field equations for the spherically symmetric perfect fluid case with shear and with vanishing acceleration. If these solutions have shear, they must necessarily be nonstatic. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three known classes of solutions. The fourth class of solutions with shear leads to a generalized Emden-Fowler equation. This equation is discussed by means of Lie's method of point symmetries.     

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.     

Exact solutions to Einstein field equations

In a recent paper Reboucas and d'Olival obtain an ordinary differential equation for a Bianchi type II metric with a rotating timelike congruence of geodesics, and obtain a particular solution of the differential equation. This paper completely integrates the differential equation.     

Global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain

We consider the equations of a viscous polytropic ideal gas in the domain exterior to a ball in ⁿ (n=2 or 3) and prove the global existence of spherically symmetric smooth solutions for (large) initial data with spherical symmetry. The large-time behavior of the solutions is also discussed. To prove the existence we first study an approximate problem in a bounded annular domain and then obtain a priori estimates independent of the boundedness of the annular domain. Letting the diameter of the annular domain tend to infinity, we get a global spherically symmetric solution as the limit.Dedicated to Professor Rolf Leis on the occasion of his 65th birthdaySupported by the SFB 256 of the Deutsche Forschungsgemeinschaft at the University of Boon.     

Spherically symmetric similarity solutions of the Einstein field equations for a perfect fluid

Spherically symmetric space-times which admit a one parameter group of conformal transformations generated by a vector such that _;v + _v; =2g _v are studied. It is shown that the metric coefficients of such space-times depend essentially on the single variablez=r/t wherer is a radial coordinate andt is the time. The Einstein field equations then reduce to ordinary differential equations. The solutions of these equations are analogous to the similarity solutions of the classical theory of hydrodynamics. In case the source of the field is a perfect fluid whose specific internal energy is a function of temperature alone, the solution of the field equations is uniquely determined by specifying data on the time-like hypersurfacez=constant and is a similarity solution. The problem of fitting a similarity solution to another solution of the field equations across a shock described by the hypersurfacez=constant is treated. A particular similarity solution for whichw=3p obtains is shown to describe a Robertson-Walker space-time. This solution is fitted to a special static solution of the Einstein field equations which has a singularity atr=0. The resulting solution of the Einstein field equations is shown to be regular everywhere except atr=0t and the shock. The special Robertson-Walker metric is also fitted to a particular class of collapsing dust solutions (which are also similarity solutions) across a shock. The resulting solution is regular everywhere except atr=t=0 and on the shock.This work was supported in part by the United States Atomic Energy Commission under contract number AT(04-3)-34 Project Agreement No. 125. It was completed when one of the authors (A.H.T.) was on sabbatical leave from the University of California, Berkeley and in residence at the Department of Applied Mathematics and Theoretical Physics, Cambridge University.     

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.     

General solution of the spherically symmetric Yang-Mills equations

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

On Chelnokov-Zeitlin solutions to the vacuum Einstein equations

The equivalence of the Chelnokov-Zeitlin solutions to the vacuum Einstein equations with a special class of Lewis solutions is established in a direct way. Also, an oversight on the signature of the solutions is pointed out and corrected.     

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.     

New stiff matter solutions to Einstein equations

New exact solutions are presented to the Einstein field equations which are spherically symmetric and static, with a perfect fluid distribution of matter satisfying the equation of state=p. One of the obtained solutions may only be used locally, the other represents the stellar interior globally and is singularity-free.