The charged line-mass in general relativity

Abstract

The two exterior solutions for a charged line-mass are examined. In both cases the mass per unit length is negative.

Higher dimensional cylindrical or Kasner type electrovacuum solutions

“…For vacuum Levi-Civita solution [8], the parameter σ is related with the mass per unit length of the source generating cylindrical vacuum and when σ > 0 the source attracts the surrounding test particles and for negative σ it repells them [60,61]. It is known for four dimensions [63] that the presence of radial electrical field dramatically changes this behaviour. Here we will show that this is indeed the case for D > 4 as well.…”

Cylindrically symmetric Brans–Dicke–Maxwell solutions

“…In that case (22) yields φ(r ) ∼ ln r immediately. With the ansatz (12) or (13) for the metric, all the field equations need to be solved simultaneously yielding different field components as functions of the radial coordinate r . The metric function W (r ) determines the conicity of the spacetime, which in turn yields a different behavior for the scalar field φ(r ).…”

“…Bonnor investigated the radial geodesics of a test particles on the spacetime of charged and cylindrically symmetric solutions and observed the following result: the well-known fact that source has positive mass density and that it applies attractive force for σ > 0 changes in the presence of a radial electrical field [12]. If there is a radial electric field, the force on a test particle becomes repulsive and the mass density is negative for σ > 0.…”

“…When the null radiation vanishes, this solution reduces to the vacuum Levi-Civita solution and the derivation of this solution is straightforward [3]. Now consider the metric (12).…”

“…Some thin shell type of sources [11] constructed as a source of these solutions and concluded that for solutions with purely electrical field these shells do not satisfy the energy conditions whereas for solutions having purely magnetic fields these conditions can be satisfied for certain range of the parameter of the vacuum Levi-Civita solution. Recently, Bonnor [12] investigated the radial geodesics of test particles for two different cylindrically symmetric electrovac solutions [13], concluding that mass per coordinate length is negative for both of the models.…”