The exterior solution for an arbitrary charged, massive source, is studied as a static deviation from the Reissner-Nordstrøm metric. This is reduced to two coupled ordinary differential equations for the gravitational and electrostatic potential functions. The homogeneous equations are explicitly solved in the particular case q2 = m2, obtaining a multipole expansion with radial hypergeometric d...

We construct static axially symmetric solutions of SU(2) Einstein-Yang-Millsdilaton theory. Like their spherically symmetric counterparts, these solutions are nonsingular and asymptotically flat. The solutions are characterized by the winding number n and the node number k of the gauge field functions. For fixed n with increasing k the solutions tend to “extremal” Einstein-Maxwell-dilaton black...

In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation (Abraham model) for any finite-energy data. As time goes to infinity, we prove that the speed of the particle converges to a certain limit, whereas the electromagnetic field can be decomposed into a soliton plus a free solution of the Maxwell equation. It is th...

Nonlocal symmetries are obtained for Maxwell’s equations in three space–time dimensions through the use of two potential systems involving scalar and vector potentials for the electromagnetic field. Corresponding nonlocal conservation laws are derived from these symmetries. The conservation laws yield nine functionally independent constants of motion which cannot be expressed in terms of the co...

We express Maxwell’s equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two equations give rise to a remarkable dual set of equations in which the operators become the matrices and the vectors become the fields. The decoupling of the equati...

Two solutions of the coupled Einstein-Maxwell field equations are found by means of the Horský-Mitskievitch generating conjecture. The vacuum limit of those obtained classes of spacetimes is the seed γ-metric and each of the generated solutions is connected with one Killing vector of the seed spacetime. Some of the limiting cases of our solutions are identified with already known metrics, the r...

For a monopole, the analogue of the Lorentz equation in matter is shown to be f = g (H − v × D). Dual-symmetric Maxwell equations, for matter containing hidden magnetic charges in addition to electric ones, are given. They apply as well to ordinary matter if the particles possess T-violating electric dipole moments. Two schemes of experiments for the detection of such moments in macroscopic pie...

We derive source-free Maxwell-like equations in flat spacetime for any helicity j by comparing the transformation properties of the 2(2j + 1) states that carry the manifestly covariant representations of the inhomogeneous Lorentz group with the transformation properties of the two helicity j states that carry the irreducible representations of this group. The set of constraints so derived invol...

A Carleman estimate for the stationary anisotropic Maxwell system is established. Its proof adopts a technique pioneered by Calderón to an overdetermined systems with rough coefficients. As an application, the conditional stability of the Cauchy problem is discussed.