Stationary axially symmetric electrovac solutions in the general scalar-tensor theory

A method is presented which reduces the Bergmann-Wagoner-Nordtvedt field equations for a stationary axisymmetric electrovac space-time, to the Einstein-Maxwell equations. In this formalism the solution generation technique of Singh and Rai for Brans-Dicke theory yields a particular class of solutions, for which the conformal scalar field depends upon the radial coordinate only. As an application of the method, new cylindrically symmetric and nonstatic scalar-Maxwell solutions are obtained for null and non-null electromagnetic fields.     

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.     

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.     

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.     

Static and stationary axially symmetric gravitational fields of bounded sources II. solutions obtainable from Weyl's class

This paper shows that a new class of axially symmetric static electrovacuum/magnetovacuum solutions is obtainable from Weyl's class of static vacuum solutions. The new class contains an infinite set of asymptotically flat solutions (in closed form) each of which involves an arbitrary set (d, _i) of parameters. These parameters have to be interpreted as functions of massm, chargee, and higher electric/magnetic multipole moments _i of the particle. The cased = 0, _i =0 leads to the Darmois solution and the cased = 0, _i 0 leads to the results of [1]. The case d=0, e=_i=0 leads to the Schwarzschild solution, the cased 0, _i =0,e 0 leads to the Reissner-Nordström solution. To get more general examples is a lengthy but straightforward exercise.     

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.     

The axially symmetric non-rotating vacuum solutions of Rosen's equations

It is shown that all axially symmetric non-rotating solutions of Rosen's field equations can be expressed in terms of two harmonic functions as well as that the total energy of Rosen's metric isMc ².     

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.     

Static spherically symmetric solutions in general projective relativity

Static spherically symmetric solutions have been obtained for general projective relativity withn=0 andn0 both in isotropic and curvature coordinates. In curvature coordinates, only a restricted exact solution is possible. However, an approximate solution can always be obtained following a method similar to Vanden Bergh. In these spacetimes there is no horizon, but only a naked singularity atr=0. Thus there are no black holes. It is shown that there is no solution in static, spherically symmetric, conformally flat spacetime.     

Axially symmetric solutions in general scalar-tensor theory

We generalise Ernst's derivation of the axially symmetric solutions of Einstein's field equations to the general scalar-tensor theory proposed by Nordtvedt. The solution of the Nordtvedt theory differs by a conformai transformation from the Brans-Dicke solution. The Kerr-like solution of the Nordtvedt theory is obtained as an example.     

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.     

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.     

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.     

Spherically symmetric static solutions in the Einstein-Cartan theory

The system of Einstein-Cartan equations has been solved in [1] in the case of zero pressure of matter and a cosmological term equal to zero. It has been shown that the gravitational spin-spin interaction exerts a stabilizing effect on the matter distribution similarly to Einstein's -term.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 60–64, September, 1982.In conclusion the author expresses his sincere gratitude to his own scientific supervisor for the doctorate of physicomathematical sciences, senior scientist V. N. Ponomarev, for his guidance and help in this research.     

Charged axially symmetric solution and energy in teleparallel theory equivalent to general relativity

An exact charged solution with axial symmetry is obtained in the teleparallel equivalent of general relativity. The associated metric has the structure function G(ξ)=1-ξ²-2mAξ³-q²A²ξ⁴. The fourth order nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad whose metric has the structure function in a factorizable form (1-ξ²)(1+r₊Aξ)(1+r_-Aξ) with r_± as the horizons of Reissner–Nordström space-time. This new form has the advantage that its roots are now trivial to write down. Then, we study the singularities of this space-time. Using another coordinate transformation, we obtain a tetrad field. Its associated metric yields the Reissner–Nordström black hole. In calculating the energy content of this tetrad field using the gravitational energy-momentum, we find that the resulting form depends on the radial coordinate! Using the regularized expression of the gravitational energy-momentum in the teleparallel equivalent of general relativity we get a consistent value for the energy.     

Tomography in external axially symmetric field

The generalization of the Cormack algorithm for inversion of the Radon transform with axially symmetric absorption is proposed. The Radon transform is one of the main mathematical tools of optical tomography. In many technical applications, the absorption is axially symmetric. This allows one to perform the expansion of the original and its image in terms of angular harmonics, which simplifies the inversion of the transform.     

Stationary axially symmetric Brans-Dicke-Maxwell fields

A method is presented which enables one to obtain solutions to the stationary axially symmetric Brans-Dicke fields coupled to source-free Maxwell fields from the solutions of the Einstein-Maxwell equations in Einstein's theory. The Brans-Dicke analog of the Kerr-Newman solution has been obtained as an example.