Stationary Einstein-Maxwell Fields Research Articles

The Simon and Simon–Mars tensors for stationary Einstein–Maxwell fields

Modulo conventional scale factors, the Simon and Simon–Mars tensors are defined for stationary vacuum spacetimes so that their equality follows from the Bianchi identities of the second kind. In the nonvacuum case one can absorb additional source terms into a redefinition of the Simon tensor so that this equality is maintained. Among the electrovacuum class of solutions of the Einstein–Maxwell equations, the expression for the Simon tensor in the Kerr–Newman–Taub–NUT spacetime in terms of the Ernst potential is formally the same as in the vacuum case (modulo a scale factor), and its vanishing guarantees the simultaneous alignment of the principal null directions of the Weyl tensor, the Papapetrou field associated with the timelike Killing vector field, the electromagnetic field of the spacetime and even the Killing–Yano tensor.

Generation of heterotic string theory solutions from the stationary Einstein–Maxwell fields

A new formalism for construction of the stationary solutions is developed for the four-dimensional gravity coupled to the dilaton, Kalb-Ramond and two Maxwell fields in a low-energy heterotic string theory form. The result of generation is automatically invariant in respect to subgroup of the stationary charging symmetry transformations; the generation can be started from the stationary Einstein-Maxwell fields. The formalism is given both in real and new compact complex form, the result of maximal symmetry extension of the stationary Einstein-Maxwell theory to discussing string gravity model is explicitly written down.

The rotation axis for stationary and axisymmetric space-times

A set of 'extended' regularity conditions is discussed which have to be satisfied on the rotation axis if the latter is assumed to be also an axis of symmetry. For a wide class of energy-momentum tensors these conditions can hold at the origin of the Weyl canonical coordinate. For static and cylindrically symmetric space-times the conditions can be derived from the regularity of the Riemann tetrad coefficients on the axis. For stationary space-times, however, the extended conditions do not necessarily hold, even when 'elementary flatness' is satisfied and when there are no curvature singularities on the axis. The authors generalise the result by Davies and Caplan (1971) for cylindrically symmetric stationary Einstein-Maxwell fields, by proving that only Minkowski space-time and a particular magnetostatic solution possess a regular axis of rotation. Further, several sets of solutions for neutral and charged, rigidly and differentially rotating dust are discussed. In most cases only very narrow classes of solutions satisfy the extended requirements.

The multipole expansion of stationary Einstein–Maxwell fields

The stationary Einstein–Maxwell equations are rewritten in a form which permits the introduction of (Geroch-) multipole moments for asymptotically flat solutions. Some known theorems on the moments in the stationary case are generalized to include Einstein–Maxwell fields.

Obtaining stationary Einstein-Maxwell fields. II

The Demianski algorithm is used to obtain stationary, axially symmetric electrovacuum fields. The possibility is analyzed of obtaining new exact stationary solutions of the Einstein-Maxwell equations by combining the Demianski algorithm with the well-known Kinnersley method.

Obtaining stationary Einstein-Maxwell fields. I

Obtaining stationary Einstein-Maxwell fields. I

Equilibrium—Its connection to global integrability conditions for stationary Einstein-Maxwell fields

This paper describes the intimate connection between global integrability conditions and equilibrium conditions for stationary Einstein-Maxwell fields. Regularity conditions are deduced for all the presently known classes of solutions.

Two-parameter static and five-parameter stationary solutions of the Einstein-Maxwell equations

The solutions of static axially symmetric Einstein-Maxwell equations corresponding to the series of stationary axially symmetric solutions for gravitational fields of spinning masses obtained by Tomimatsu and Sato are considered. This class of two-parameter solutions representing a system with mass and electric or magnetic dipole are extended through Kinnersley’s method of generating stationary Einstein-Maxwell fields. It is shown that all the solutions thus extended have the same behaviour in the distant region and describe a source with mass, electric charge, magnetic dipole, higher multipoles of all three kinds and angular momentum.

Five-Parameter Exterior Solution of the Einstein-Maxwell Field Equations

A five-parameter solution of the combined Einstein-Maxwell equations is given which describes a source containing mass, electric charge, magnetic dipole, higher multipole moments of all three kinds, and angular momentum. The solution is obtained by using Kinnersley's method of generating stationary Einstein-Maxwell fields from known solutions of the Einstein-Maxwell equations. We start with a two-parameter solution of a system having mass and a magnetic dipole moment discovered by Misra, Pandey, Srivastava, and Tripathi. All solutions discussed in this paper are asymptotically flat, and all have infinite red-shift surfaces that are singular. Possible relevance of these solutions to black-hole physics is remarked upon.