Static and time-dependent solutions of Einstein-Maxwell-Yukawa fields

An exact solution of Einstein-Maxwell-Yukawa field equations has been obtained in a space-time with a static metric. A critical analysis reveals that the results previously obtained by Patel [9], Singh [10], and Taub [11] are particular cases of our solution. The singular behavior of the solutions has also been discussed in this paper. Further, extending the technique developed by Janis et al. [12], for static fields, to the case of nonstatic fields, an exact time-dependent axially symmetric solution of EMY fields has been obtained. Our solution in the nonstatic case is nonsingular in the sense of Bonnor [15] and presents a generalization of the results obtained by Misra [7] to the case when a zero-mass scalar field coexists with a source free electromagnetic field.     

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.     

Non-existence of axially symmetric massive scalar fields

It has been observed that for the axially symmetric Einstein-Rosen metric, the stress-tensor of a scalar meson field associated with meson of rest mass cannot be the source term for generating gravitation. The above result also holds even when this meson field is coupled with an electromagnetic field.     

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.     

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.     

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.     

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.     

Nonlinear transverse-wave interactions in divergent axially symmetric magnetic fields

The dynamics of transverse-wave interactions in intense electron beams in divergent axially symmetric magnetic fields has been investigated by computer simulation. The case of a short magnetic field was analyzed. The conversion of electron-beam transverse waves in the presence of a decelerating electric field was considered.     

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.     

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.     

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.     

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.     

On static,axially symmetric Einstein-Maxwell fields. Part I

The Weyl solution of the problem, obtained on the assumption thatg ₀₀ is a function of the electrostatic potential, is varied and the linearized field equations for the variation are discussed. The complete solution of the problem is determined for the special case of the Weyl solution that generalizes the Reissner-Nordstrom solution withm = ¦e¦.     

On static,axially symmetric Einstein-Maxwell fields. Part II

Starting from the Reissner-Nordström solution withm =e we consider a variation representing a second particle situated outside the horizon. A formal dipole term in the potential of the second particle ensures equilibrium without additional stresses between the particles. The complete solution for the variation is determined and discussed in detail.     

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.     

Algebraic construction of static axially symmetric self-dual gauge fields for an arbitrary group

It is suggested that the Higgs and the Yukawa couplings of the standard model possess two global U(1)-symmetries: independent chiral rotations of quarks and leptons. The model requires the existence of two axions, one of which (massive) does not interact with leptons, whereas the second one interacts both with leptons and quarks.     

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.     

Gravitational radiation reaction in quasistatic,axially symmetric systems with possibly strong fields

The leading radiation reaction in quasistatic, axially symmetric systems is calculated by matched asymptotic expansions. Earlier results on inductive transfer of near-zone energy are combined via matching with a wave-zone expansion in the Regge-Wheeler gauge. Two independent measures of the damping are computed: (1) the change of the 1/Rcoefficient in a Weyl-Levi-Cività type of multipole expansion in the near zone and (2) the change in Bondi energy at future null infinity. When an averaging process is justified, such as in (nearly) periodic systems, both quantities yield a generalized version of the usual quadrupole formula, provided the radiation is outgoing at future null infinity. It is also shown that terms nonanalytic in the slow-motion parameter make a time-even contribution to the near-zone monopole coefficient. The principal advantage of this calculation over previous work is that the sources are permitted to have strong gravitational fields. Moreover, no specific model for the sources is assumed.