Related papers: Maxwell Fields in Spacetimes Admitting Non-Null Ki…
We consider the 3-dimensional formulation of Einstein's theory for spacetimes possessing a non-null Killing field $\xi^a$. It is known that for the vacuum case some of the basic field equations are deducible from the others. It will be…
It is proven that a solution to the Einstein-Maxwell equations whose gravitational and electromagnetic radiation fields vanish is in fact stationary in a neighbourhood of spatial infinity. That is, if the Weyl and Faraday tensors decay…
A procedure for solving the Maxwell equations in vacuum, under the additional requirement that both scalar invariants are equal to zero, is presented. Such a field is usually called a null electromagnetic field. Based on the complex Euler…
We study Einstein-Maxwell (non-null) sourcefree configurations that can be extended to any conformally invariant non-linear electrodynamics (CINLE) by a constant rescaling of the electromagnetic field. We first obtain a criterion which…
In a space-time $M$ with a Killing vector field $\xi^a$ which is either everywhere timelike or everywhere spacelike, the collection of all trajectories of $\xi^a$ gives a 3-dimension space $S$. Besides the symmetry-reduced action from that…
In this paper we first analyze the structure of Maxwell equations in a Lorentzian spacetime where the potential A is proportional to 1-form K physically equivalent to a Killing vector field (supposed to exist). We show that such A obeys the…
The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic…
In this paper we are concerned to reveal that any spacetime structure <M,[g]<LaTeX>\slg</LaTeX>,D,{\tau}_{[sg]<LaTeX>\sslg</LaTeX>},\uparrow>, which is a model of a gravitational field in General Relativity generated by an energy-momentum…
We provide for the first time the exact solution of Maxwell's equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the…
We determine the class of $p$-forms $F$ which possess vanishing scalar invariants (VSI) at arbitrary order in a $n$-dimensional spacetime. Namely, we prove that $F$ is VSI if and only if it is of type N, its multiple null direction $l$ is…
In vacuum space-times the exterior derivative of a Killing vector field is a two-form that satisfies Maxwell equations without electromagnetic sources. Using the algebraic structure of this two-form we have set up a new formalism for the…
We show that a large class of null electromagnetic fields are immune to any modifications of Maxwell's equations in the form of arbitrary powers and derivatives of the field strength. These are thus exact solutions to virtually any…
We consider $d$-dimensional solutions to the electrovacuum Einstein-Maxwell equations with the Weyl tensor of type N and a null Maxwell $(p+1)$-form field. We prove that such spacetimes are necessarily aligned, i.e. the Weyl tensor of the…
We discuss Petrov type D Einstein-Maxwell fields in which both double null eigenvectors of the Weyl tensor are non-aligned with the eigenvectors of a non-null electromagnetic field and are assumed to be geodesic, shear-free, diverging and…
We revise and generalize the properties of the electric and the magnetic scalar potentials in spacetimes admitting a Killing vector field: Their constancy on the Killing horizons, uniqueness of solution for the electromagnetic test fields…
Maxwell's vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators ( integrals of motion )…
We present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the $3$-sphere $S^3$. The conformal…
The classification of the Stackel spaces of the electrovacuum of the type (3.0) has been done. These spaces are invariant under the action of the three-parameter abelian group of motions and belong to the first type Bianchi spaces. In the…
We find an explicit solution of the source free Maxwell equations in a generalized Kerr-NUT-(A)dS spacetime in all dimensions. This solution is obtained as a linear combination of the closed conformal Killing-Yano tensor $h_{ab}$, which is…
We present a general solution of the coupled Einstein-Maxwell field equations (without the source charges and currents) in three spacetime dimensions. We also admit any value of the cosmological constant. The whole family of such…