Generating Conjecture and Some Einstein-Maxwell Field of High Symmetry

Details Generating Conjecture and Some Einstein-Maxwell Field of High Symmetry Generating Conjecture and Some Einstein-Maxwell Field of High Symmetry

2000-06-20

arxiv.org/abs/gr-qc/0006069v1

Czech. J. Phys. 48 (1998) 113-116

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

3 pages, LaTeX

Scientific paper

For stationary cylindrically symmetric solutions of the Einstein-Maxwell equation we have shown that the "charged" solutions of McCrea, Chitre et al.(CGN), Van den Bergh and Wils (VW) can be obtained from the seed metrics using generating conjecture. The McCrea "charged" solution has as a seed vacuum metric the Van Stockum solution with a Killing vector (0,0,1,0). The CGN "charged" solution and the VW "charged" solution have the static seed metrics connected by the complex substitution (t --> iz), (z --> it) and the Killing vector which is a simple linear combination of ${\partial}_{\phi}$ and ${\partial}_{t}$ Killing vectors (VW), respectively ${\partial}_{\phi}$ and ${\partial}_{z}$ Killing vectors (CGN).

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