Untitled

Abstract

The method based on the Horský-Mitskievitch conjecture is applied to the Levi-Civita vacuum metric. It is shown, that every Killing vector is connected with a particular class of Einstein-Maxwell fields and each of those classes is found explicitly. Some of obtained classes are quite new. Radial geodesic motion in constructed space-times is discussed and graphically illustrated in the Appendix.

Weyl metrics and the generating conjecture

“…We are going to concentrate on electro-and magnetovacuum solutions obtained from seed axially symmetric vacuum gravitational fields [8,9]. For the static EM fields the twist potential ~5 in (2) equals zero and the potential E takes real values only (see Table 1).…”

“…for the description of gravitating discs around black holes [19,20]. All the solutions found by the authors employing HM generating conjecture revealed that for a particular class of charged solutions the metric coefficients were modified in the same way, no matter whether we start with the Levi-Civita [8] or the Darmois-Vorhees-Zipoy (also "y) [9] metrics. Let us show, that this modification represents the Harrison transformation (9) in fact.…”

“…Rewriting the magnetovacuum 7-metric line element The same could be gradually accomplished for all the solutions generated from the Levi-Civita seed metric in [8] --they represent its Harrison transformation (9). Naturally, one would like to check the spacetimes studied in [2] to support the HM conjecture.…”

“…From this point of view for all solutions generated from the seed Weyl metrics in [8,9] the HM conjecture in its generalized formulation [4] necessarily had to work and provide new EM fields. Of course, the Harrison transformation is really simple for static metrics in Section 3, where we do not need to take into account the zero twist potential ~5 in (3).…”

Generating solutions to the Einstein–Maxwell equations

“…The so called Horsky-Mitskievich conjecture, outlines an efficient and fruitful way to obtain solutions to the E-M equations, as a generalization of some already known vacuum seed metrics. In this context, taking the γ-solution as a seed vacuum spacetime, they have obtained two classes of E-M fields, the main properties of which are discussed extensively in [10] and [11].…”