Charged universes of the Gödel type with closed timelike curves

Abstract

The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, in particular their properties from a chronological point of view. Each of our spacetimes is stationary and cylindrically symmetric and is filled with a perfect fluid that is electrically charged. There are two classes of solutions and examples of each are investigated. We give examples of the first class for both the vanishing and non-vanishing Lorentz force.

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“…Case I consists of the Wright solution alternative source (3.1) and the generalization (3.5) of the Lorentz force-free solutions in [9,11]. Case II describes charged dust solution (3.10) which is cylindrically symmetric spacetime but not regular at the origin.…”

“…Scalar field becomes equal to φ = φ 0 + φ 1 z and does not enter the energy density, which could be expected because of the lack of interaction between charged fluid and scalar field. If both φ 1 and φ 2 are zero, (3.5) convertes to Lorentz force-free solution presented in [11,9].…”

“…(ii) Purely complex substitution α → iα in previous case gives the metric figure 1 and [11,14] for details). Influence of the magnetic field to the chronology violation is positive unlike the scalar field influence, that is negative.…”

“…Metrics (4.1) or (4.3) suffer from singularities forC < 0 when r goes to infinity, whereas Riemann tensor invariants of (4.2) are well behaved (see [11]). Moreover (4.1) as well as (4.3) are radially bounded in the sense that the proper radial distance d of infinity r → ∞ from the rotation axis is finite unlessC = 0 (figure 2).…”

“…Physical interpretation of Lorentz force-free charged fluids in general relativity can be found in [10]. Recently, Klepáč and Horský submitted G 3 spacetimes for generally non-vanishing Lorentz force [11].…”