Axially symmetric Brans-Dicke-Maxwell solutions

Following a method of John and Goswami new solutions of coupled Brans-Dicke-Maxwell theory are generated from Zipoy's solutions in oblate and prolate spheroidal coordinates for source-free gravitational field. All these solutions become Euclidean at infinity. The asymptotic behavior and the singularity of the solutions are discussed and a comparative study made with the corresponding Einstein-Maxwell solutions. The possibility of a very large red shift from the boundary of the spheroids is also discussed.     

General magnetized Weyl solutions: disks and motion of charged particles

We construct three families of general magnetostatic axisymmetric exact solutions of Einstein-Maxwell equations in spherical coordinates, prolate, and oblates. The solutions obtained are then presented in the system of generalized spheroidal coordinates which is a generalization of the previous systems. The method used to build such solutions is the well-known complex potential formalism proposed by Ernst, using as seed solutions vacuum solutions of the Einstein field equations. We show explicitly some particular solutions among them a magnetized Erez-Rosen solution and a magnetized Morgan-Morgan solution, which we interpret as the exterior gravitational field of a finite dislike source immersed in a magnetic field. From them we also construct using the well known “displace, cut and reflect” method exact solutions representing relativistic thin disks of infinite extension. We then analyze the motion of electrically charged test particles around these fields for equatorial circular orbits and we discuss their stability against radial perturbations. For magnetized Morgan-Morgan fields we find that inside of disk the presence of magnetic field provides the possibility of to find relativist charged particles moving in both prograde and retrograde direction.     

Axially symmetric electrovac solution

Using oblate and prolate spheroidal co-ordinates static axisymmetric solutions of the coupled Einstein-Maxwell equations are obtained in vacuo. The solutions are asymptotically flat and reduce to the electrically neutral solution of Zipoy when one of the constants vanishes. As a special case the solutions reduce to the ones generated from Bonnor's theorem. Our solutions are also shown to give arbitrarily large gravitational redshifts under certain conditions.The author wishes to thank Prof. S. Banerjee, The University of Burdwan, for helpful discussions and also the University Grants Commission for financial assistance. The useful suggestions of the referee are also acknowledged.     

An Infinite Family of Magnetized Morgan-Morgan Relativistic Thin Disks

Applying the Horsky-Mitskievitch conjecture to the empty space solutions of Morgan and Morgan due to the gravitational field of a finite disk, we have obtained the corresponding solutions of the Einstein-Maxwell equations. The resulting expressions are simply written in terms of oblate spheroidal coordinates and the solutions represent fields due to magnetized static thin disk of finite extension. Now, although the solutions are not asymptotically flat, the masses of the disks are finite and the energy-momentum tensor agrees with the energy conditions. Furthermore, the magnetic field and the circular velocity show an acceptable physical behavior.     

Axially symmetric electrovac solutions

Two classes of electrovac solutions are obtained in oblate spheroidal coordinates, which are the electromagnetic analogs of Zipoy's monopole and dipole solutions. The asymptotic behavior of the solutions is studied to gain some insight into the nature of the source of the gravitational and electromagnetic fields. A similar stationary solution of the pure gravitational field is found to belong to Papapetrou's class.     

Solutions of the Einstein-Maxwell equations with many black holes

In Newtonian gravitational theory a system of point charged particles can be arranged in static equilibrium under their mutual gravitational and electrostatic forces provided that for each particle the charge,e, is related to the mass,m, bye=G ^1/2 m. Corresponding static solutions of the coupled source free Einstein-Maxwell equations have been given by Majumdar and Papapetrou. We show that these solutions can be analytically extended and interpreted as a system of charged black holes in equilibrium under their gravitational and electrical forces.We also analyse some of stationary solutions of the Einstein-Maxwell equations discovered by Israel and Wilson. If space is asymptotically Euclidean we find that all of these solutions have naked singularities.Alfred P. Sloan Research Fellow, supported in part by the National Science Foundation.     

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.     

Kerr-Newman metric in deSitter background

In addition to the Kerr-Newman metric with cosmological constant several other metrics are presented giving Kerr-Newman type solutions of Einstein-Maxwell field equations in the background of deSitter universe. The electromagnetic field in all the solutions is assumed to be source-free. A new metric of what may be termed as an electrovac rotating de-Sitter space-time—a space-time devoid of matter but containing source-free electromagnetic field and a null fluid with twisting rays—has been presented. In the absence of the electromagnetic field, our solutions reduce to those discussed by Vaidya.     

Some solutions of the Einstein-Maxwell equations in general relativity

A solution of the Einstein-Maxwell equations corresponding to source-free electromagnetic field plus pure radiation is obtained. The solution is algebraically special. A particular case of the solution is considered which encompasses many known solutions. Among them is a radiating Ruban metric.     

Factor structure of the Tomimatsu‐Sato solutions and their recurrence relations

We consider stationary axisymmetric vacuum solutions of Einstein's equations for which the Ernst potential is rational in prolate spheroidal coordinates. Extending an earlier study we show that there are several new expressions which are factorizable. In particular, we concentrate on the Tomimatsu‐Sato solutions and their recurrence relations. Various continuum limits of the recurrence relations will be discussed.     

New exact Einstein-Maxwell fields for a massless charge

New solutions of the Einstein-Maxwell equations are presented. The solutions describe the gravitational fields of a massless charge.     

Generalized plane gravitational waves

The definition of plane gravitational waves is generalized to include the case in which rays are not orthogonal to the two-dimensional wave surfaces. All Einstein spaces and some new solutions of the Einstein-Maxwell equations of this type are given.     

Application of the pattern equation method in spheroidal coordinates to solving diffraction problems with highly prolate scatterers

Acoustical Physics - The equations of the diagram equation method are formulated in terms of prolate spheroidal coordinates. Examples of the convergence and stability of numerical algorithms based...     

Majumdar-Papapetrou class of nonstatic cylindrically symmetric Brans-Dicke-Maxwell fields

We have obtained relations between certain components of the metric and the electromagnetic potentials for source-free Brans-Dicke-Maxwell fields described by a nonstatic cylindrically symmetric Einstein-Rosen metric. These are important, in the sense that they generate a class of solutions that in a way can be said to belong to the class generated by similar relations obtained by Majumdar [1] and Papapetrou [2] for generalized static Einstein-Maxwell fields. The relations have further been used to reduce the B-D Maxwell equations to B-D vacuum equations and vice versa.     

Coulomb Sturmians in spheroidal coordinates and their application for diatomic molecular calculations

Coulomb Sturmians are obtained in prolate spheroidal coordinates by separation of variables in the Schrödinger equation and direct solution of the appropriate one-dimensional equations. Molecular orbitals are expressed as linear combinations of the introduced Coulomb Sturmians and some low-lying energy terms and corresponding wave functions are calculated for one-electron diatomic molecules. It is shown that similarity of the one- and two-centre orbitals in spheroidal coordinates, combined with completeness and good convergence properties of Coulomb Sturmians, substantially speeds up convergence and makes the calculated results closer to the exact ones. Application of the elaborated calculating scheme for diatomic many-electron molecules is discussed.     

Explicit spheroidal wave functions of the hydrogen atom

A simple and straightforward calculating scheme is suggested for finding wave functions of the hydrogen atom in prolate spheroidal coordinates. The wave functions are found in an explicit form by the direct solution of appropriate one-dimensional equations. The suggested calculating scheme allows us to carry out simple calculations and to obtain spheroidal wave functions in principle for arbitrary eigenstates of the hydrogen atom. Expansions are found for the obtained spheroidal wave functions over a spherical basis.     

Non-spherical quasi-black holes

Quasi-black holes are objects having some of the properties of black holes but which have no horizon and are non-singular. Up till now those found have been spherical. I give solutions of the Einstein–Maxwell equations representing spheroidal quasi-black holes, made of electrically counterpoised dust. They contain a parameter a which governs the external gravitational and electrical fields of the spheroid: as a tends to zero those fields become spherical in spite of the spheroidal character of the source.     

Bianchi type V perfect fluid models with source-free electromagnetic fields

The Einstein-Maxwell Field equations characterizing a nontitled Bianchi type V perfect fluid model with source-free electromagnetic field are solved exactly in the nonlocally rotationally symmetric case. It is found that these equations admit one and only one exact solution, expressible, however, in terms of two arbitrary functions.     

Electromagnetic Bianchi cosmologies

All exact solutions of the Einstein-Maxwell equations of Bianchi type-I which are of physical importance have been found. The solutions represent non-locally rotationally symmetric universes with source-free electromagnetic fields and the matter content is a perfect fluid, with equation of state p=(γ?1)?(1?γ?2). Non-titled Bianchi type-II models are integrated for perfect fluid matter for all values of γ.