New axially symmetric solutions of the Einstein-Maxwell equations

New exact solutions of the algebraic form for the static Einstein-Maxwell equations representing the exterior gravitational field of a massive magnetic dipole are derived. They are then used for construction of the stationary electrovacuum solutions reducing to the Schwarzschild metric in a pure vacuum limit.     

On axially symmetric solutions to the Higgs-Kibble-Yang-Mills field equations

The field equations for axially symmetric generalizations of the 't Hooft-Polyakov magnetic monopole are written out in a preferred coordinate system. It is argued that no soliton solutions exist when the product 2eg of the electric chargee with the magnetic chargeg is an even integer.Dedicated to Achille Papapetrou on the occasion of his retirement.     

Non-existence of higher dimensional axially symmetric field in Rosen's theory of gravitation

In Rosen's bimetric theory of gravitation the non-existence of higher dimensional axially symmetric massive scalar field and massive complex scalar field coupled with electromagnetic field is established.The authors are thankful to the referee for helpful suggestions.     

On axially symmetric soliton solutions of the coupled scalar-vector-tensor equations in general relativity

The inverse scattering theory used by Belinsky and Zakharov to obtain soliton solutions of the of the Einstein equations is here applied to the case of a five-dimensional space and interpreted in the framework of the Jordan-Kaluza-Klein theory. For two solitons exact, stationary, axially symmetric and asymptotically flat solutions are obtained.     

Axially symmetric solution to Rosen's field equations with angular momentum

There has been no Kerr-like solution to Rosen's bimetric theory of gravity, in the sense that there is no stationary, axially symmetric solution with angular momentum term. Here such a solution is derived and investigated.     

An investigation of axially symmetric electrovac solutions

For the axially symmetric, electrostatic vacuum problem, there are three unknowns:g ₀₀,g ₁₁, and , the electrostatic field. Herlt, using his generation methods, has presented several new solutions by explicitly givingg ₀₀ and only. Theg ₁₁ is now determined in two cases and a detailed discussion of these solutions is given. The solutions do not, in general, possess the overlapping equipotential structure [g ₀₀=g ₀₀()] which characterizes the Weyl class. One of the classes contains metrics which can be physically interpreted as representing exterior space-times of non-Weyl two-body-type charged point sources. With the specialization of the arbitrary parameters, the above solutions do reduce to known Weyl solutions. The Bonnor solution is a member of one of the above classes and consequently a possible physical reinterpretation of this solution is given. Kinnersley transformations applied to the above classes yield stationary space-times with line singularities and NUT-like asymptotic behavior.     

The harmonic-map structure of the axially symmetric stationary Einstein equations

We systematically review the solutions of the vacuum Einstein equations for the axially symmetric stationary case which are harmonic maps. In particular, we show that the interesting part of the Kerr solution is a composition of a harmonic map intoH ₁ ² with a totally geodesic map fromH ₁ ² into SS(1,1). We also point out, relying on Sanchez' results, that there is an analogous structure for the Lorentz-domain cases involving cylindrical gravitational waves and colliding plane waves.     

Bäcklund transformations and exact solutions of the stationary axially symmetric Einstein equations

The Bäcklund transformations of the self-dual Yang-Mills fields are used to derive exact solutions of the stationary axially symmetric Einstein equations. Three solutions which belong to an infinite series of such solutions are explicitly calculated, the first of which is the Lewis solution. Also the first of another infinite series of solutions is calculated, which for some value of a parameter becomes the Papapetrou solution.     

Static axially symmetric solutions in Nordtvedt's theory

Static axially symmetric solutions in vacuum are obtained in the general scalar-tensor theory proposed by Nordtvedt. The solutions are asymptotically flat and under certain conditions give very large red shift. The asymptotic behavior and singularity are studied and a comparison is made with a corresponding solution with spherical symmetry. It is also observed that with a conformal transformation the Nordtvedt metric appears to reduce to the Brans-Dicke one.     

A new construction technique for exact axially symmetric static electrovac solutions of the Einstein-Maxwell equations

Coordinates adapted to the full electrostatic symmetries of a charged axially symmetric static system are constructed and applied to the coupled Einstein-Maxwell equations. A new solution is presented and the framework for general solutions is developed. The Weyl solutions g₀₀(Φ) are readily extracted from the formalism.     

Conformally symmetric vacuum solutions of the gravitational field equations in the brane-world models

A class of exact solutions of the gravitational field equations in the vacuum on the brane are obtained by assuming the existence of a conformal Killing vector field, with non-static and non-central symmetry. In this case, the general solution of the field equations can be obtained in a parametric form in terms of the Bessel functions. The behavior of the basic physical parameters describing the non-local effects generated by the gravitational field of the bulk (dark radiation and dark pressure) is also considered in detail, and the equation of state satisfied at infinity by these quantities is derived. As a physical application of the obtained solutions we consider the behavior of the angular velocity of a test particle moving in a stable circular orbit. The tangential velocity of the particle is a monotonically increasing function of the radial distance and, in the limit of large values of the radial coordinate, tends to a constant value, which is independent on the parameters describing the model. Therefore, a brane geometry admitting a one-parameter group of conformal motions may provide an explanation for the dynamics of the neutral hydrogen clouds at large distances from the galactic center, which is usually explained by postulating the existence of the dark matter.     

Non-existence of stationary,axially symmetric,asymptotically flat solutions of the Einstein equations for dust

It is shown that the Einstein equations for stationary, axially symmetric distributions of dust do not admit regular, asymptotically flat solutions, provided the mass density is strictly positive everywhere.     

Time dependent axially symmetric solutions of the Einstein-Maxwell-Yukawa fields

Extending a technique developed for static fields by Janiset al. [10] to the nonstatic fields two exact solutions in the case of Einstein-Rosen metric for the interacting electromagnetic and zero mass scalar fields have been obtained.     

On Bianchi type-I vacuum solutions inR+R 2 theories of gravitation. II. The axially symmetric anisotropic case

The field equations following from a LagrangianL(1/L)(–g)^1/2[(1/2)R+l ²(R _lk R ^lk +R ²)] will be considered for Bianchi type-I homogeneous models. Thereby the special case,+3=0, is considered qualitatively for axially symmetric anisotropic metrics. Generically, the solutions have both past and future singularities, but it will be proven by topological arguments that the two-dimensional space of solutions possesses a one-parameter subspace of solutions with a behavior similar to the Kasner solution.     

On axially symmetric solutions of Einstein's field equations in matter and an example of static gravitational shielding

A model system, consisting of a thin spherical shell with radiusR and massM and a point massm at a distances>R from the center of the sphere, held fixed by an appropriate strut, is solved to ordermM. The stresses in the shell are not of the canonical Weyl type, and it is argued that the same is true for more realistic situations, e.g., rotating matter. Owing to the nonlinearity of Einstein's field equations, the field of the point mass is shielded from the interior of the shell by a factor lying between 1–3M/R and 1–2M/R, and the field outside the shell explicitly depends onR.     

On stationary axially symmetric interior solutions in general relativity

This note presents the coordinate transformation by which the coordinate condition of a previous paper (Rawson-Harris, 1972) may be imposed.     

Axially symmetric solutions of einstein equations

Two exact axially symmetric solutions of the gravitational field equations, which depend on a number of arbitrary real constants, are derived.     

Einstein equations and inertial forces in axially symmetric stationary spacetimes

We investigate the relations between the inertial forces and the Einstein equations in axially symmetric stationary spacetimes. For the vacuum stationary axially symmetric spacetimes, we use the Geroch formalism to express the Einstein equations in terms of inertial forces. For the spacetimes with the perfect fluid sources, we use the formalism developed by Hansen and Winicour for establishing the relations. As expected intuitively, the gradients of inertial forces represent the field equations.     

Exact solutions of vacuum Brans-Dicke equations

Vacuum Stäckel type (2.1) spaces are classified in Brans-Dicke theory for the case when the scalar field depends on all the variables.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 86–90, January, 1992.