The magnetic field of a current carrying cosmic string

Abstract

The magnetostatic field of an infinite rectilinear current placed in the stationary gravitational field of a rotating cosmic string is found. An interesting aspect of this problem is that although the metric is mathematically very simple, its physical meaning is not trivial. It depends only on topological parameters. So, the cosmic string vacuum space-time is locally equivalent to the Minkowski space-time, but not globally. The calculations are so simple that they can easily be shown in the classroom.

Static Cylindrical Symmetric Solutions in the Einstein-Aether Theory

“…It might as well be on the geometry-side where the effect of the aether vector field is due to the fact that the coupling constant of the EA theory is different from that one of GR. So, it is unfortunate if one gets an impression that EA theory is simply GR coupled to vector field because of equation (11).…”

“…The importance of the second emerges from its global topological meaning, since it cannot be removed by scale transformations [2,6,7]. It produces a gravitational analog for the Aharanov-Bohm effect that allows an unobservable quantity (Newtonian) (the constant potential beyond Newtonian potential) to become observable in relativistic theory through angular deficit chains [6,7,8,9,10,11,12]. However, the first independent parameter, understood as Newtonian mass per unit length for small densities of matter, whose interpretation for higher mass densities is very difficult.…”

Effects of torsion on electromagnetic fields

“…A similar problem was handled by M.F.A. da Silva et al [7,8], who calculated the magnetostatic field due to an electric current placed in the gravitational background of a rotating cosmic string. In their work, torsion comes from rotation, thus coupling time to the angular coordinate φ.…”

“…This increases the density of field lines therefore corresponding to an amplification of the electric field amplitude. This should be compared to the amplification found in the magnetostatic field of a current-carrying cosmic string [7]). …”

Translation in cylindrically symmetric vacuum

“…The importance of the second one emerges from its global topological meaning since it cannot be removed by scale transformations [3,7,8]. It produces a gravitational analog to the Aharanov-Bohm effect which allows a (Newtonian) non observable quantity (the additional constant potential to the Newtonian potential) to become observable in the relativistic theory through angular deficit strings [7,8,9,10,11,12,13].…”