Correction: New stiff matter solutions are really not stiff

Four new solutions in general relativity have recently been derived as representing static spherically symmetric stiff matter,=p. It is pointed out that the equation of state is, in fact,+p=0. It is further shown that two of the solutions are physically reasonable, turning out to represent the vacuum, one of them with a term.     

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.     

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.     

Exact solutions of vacuum n-dimensional Einstein equations

A class of exact solutions of the vacuum n-dimensional Einstein equations for the case in which the components of the metric tensor depend on two variables is obtained by the method of separation of variables. Particular cases of this class of solutions are considered: a plane-symmetric metric; an axisymmetric metric; metrics of the Casner type.M. V. Lomonosov State University, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 120–124, October, 1995.     

Approximate radiative solutions of the Einstein equations

In this paper the external field of a bounded source emitting gravitational radiation has been considered. A successive approximation method has been used to integrate the Einstein equations in Bondi's coordinates. A method of separation of angular variables has been worked out and the approximate Einstein equations have been reduced to the key equations (3.8)–(3.10). The losses of mass, momentum, and angular momentum due to gravitational multipole radiation have been found. It has been demonstrated that in the case of proper treatment a real mass occurs instead of a mass aspect in a solution of the Einstein equations. In Appendix C Bondi's news function has been given in terms of sources.     

Exact vacuum solutions of the Einstein equations

The vacuum Einstein equations for the Kerr-Schild metric are investigated. It is shown that they admit representation in the form of the double four-dimensional curl of the perturbation of the Euclidean metric, whereupon it is possible to note certain general directions in which to seek exact solutions. For spaces with a normal isotropic geodesic congruence the GR equations are rewritten with the application of a dyadic splitting of the metric; cases of two-dimensional subspaces of constant curvature are discussed. The investigation is illustrated by the exact nonstationary algebraic type N and anti-Schwarzschild solutions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 23–26, September, 1982.     

Monopole-quadrupole static axisymmetric solutions of Einstein field equations

An infinite family of exact solutions of the Einstein vacuum equations for the static case with axial symmetry is presented in an explicit form. Each solution of this family contains two arbitrary parametersM andQ that represent the mass and quadrupole moment of the source. In addition, each solution can be interpreted physically as the pure relativistic quadrupole correction to the Schwarzschild solution at a given multipole order.     

Space-time defect solutions of the Einstein field equations

Ideas from the theory of defects in crystalline matter are combined with results from the direct gauge theory for the Poincaré group to obtain exact solutions of the Einstein field equations. Many of the solutions are sufficiently simple that the equations for geodesic motion can be solved in closed form. Some of these solutions exhibit unexpected behaviors and properties, such as geodesic motions with hyperlight speed and local time reversals relative to observers in the asymptotic Minkowski space-time at large distances from the defect core regions. However, these same geodesic motions are regular in the frames of reference attached to observers that move along the geodesies, and hence no established physical laws are broken by such solutions.     

Discontinuities of solutions of the Einstein equations. II

Right zero-vectors of the characteristic matrix of the Einstein equations are constructed on isotropic cones. Relationships for the discontinuities of two derived functions of the field in the and surfaces are indicated. Quantities describing the weak discontinuities of solutions of the gravitational field equations are constructed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 38–41, February, 1982.     

Smooth static solutions of the Einstein/Yang-Mills equations

We consider the Einstein/Yang-Mills equations in 3+1 space time dimensions withSU(2) gauge group and prove rigorously the existence of a globally defined smooth static solution. We show that the associated Einstein metric is asymptotically flat and the total mass is finite. Thus, for non-abelian gauge fields the Yang-Mills repulsive force can balance the gravitational attractive force and prevent the formation of singularities in spacetime.Research supported in part by the NSF, Contract No. DMS 89-05205Research supported in part by the ONR, Contract No. DOD-C-N-00014-88-K-0082Research supported in part by the DOE, Grant No. DE-FG02-88ER25065Research supported in part by the U.K. Science and Engineering Research Council     

Classification of an infinite series of static solutions to the vacuum Einstein equations

We propose a classification of an infinite series of the static solutions to the vacuum Einstein equation by means of their soliton number and the real and/or complex pole trajectories. We also show that in the 4-soliton solution there appears an intriguing ring solution of which the curvature invariant has a finite limit at the rings.     

Semi-global solutions of Einstein equations,minkowskian near past infinity

On a universe homeomorphic toV ^T =]– ,T[x³, we prove the existence of solutions of Einstein equations, minkowskian near past infinity, if the sources are small enough for some norms. We prove that some of these solutions verify at least the positivity condition (Weak energy condition) on some domains homeomorphic toV ^T .     

New solutions of the Einstein equations taking into account the vacuum effects of quantized fields

The Einstein equations are solved, whose right-hand sides involve both the background matter and the vacuum effects of quantized fields. It is shown that the de Sitter model is stable with respect to perturbations due to the vacuum corrections. For all other homogeneous isotropic models, taking the vacuum polarization into account makes the singularity occur earlier.     

Use of conformal,mapping to construct new solutions of the Einstein equations

A method is obtained for constructing new solutions of the Einstein equations from known solutions, beginning with the structure of the Einstein tensor and using conformai mapping. The sollowing cases are considered: transformation of vacuum solutions into hydrodynamic solutions and the transformation of hydrodynamic solutions into solutions of the same type. A necessary and sufficient condition, imposed on the vacuum metric, is found which guarantees that solutions with a hydrodynamic energy-momentum tensor will be produced from vacuum solutions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 110–114, November, 1973.The author is deeply grateful to Ya. I. Pugachev and to the members of the seminar directed by him for discussion of the results of this paper.     

On existence and behaviour of asymptotically flat solutions to the stationary Einstein equations

We show existence and uniqueness of asymptotically flat solutions to the stationary Einstein equations inS=³–B _r , whereB _r is a ball of radiousr>0, when a small enough continuous complex function û on S is given. Regularity and decay estimates imply that these solutions are analytic in the interior ofS and also at infinity, when suitably conformally rescaled.