Levi-Civita Solutions Coupled with Electromagnetic Fields

Details Levi-Civita Solutions Coupled with Electromagnetic Fields Levi-Civita Solutions Coupled with Electromagnetic Fields

2001-04-04

arxiv.org/abs/gr-qc/0104018v1

Class.Quant.Grav. 18 (2001) 4569-4588

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Typed in Revtex, including two figures

Scientific paper

10.1088/0264-9381/18/21/312

The local and global properties of the Levi-Civita (LC) solutions coupled with an electromagnetic field are studied and some limits to the vacuum LC solutions are given. By doing such limits, the physical and geometrical interpretations of the free parameters involved in the solutions are made clear. Sources for both the LC vacuum solutions and the LC solutions coupled with an electromagnetic field are studied, and in particular it is found that all the LC vacuum solutions with $\sigma \ge 0$ can be produced by cylindrically symmetric thin shells that satisfy all the energy conditions, weak, dominant, and strong. When the electromagnetic field is present, the situation changes dramatically. In the case of a purely magnetic field, all the solutions with $\sigma \ge 1/\sqrt{8}$ or $\sigma \le - 1/\sqrt{8}$ can be produced by physically acceptable cylindrical thin shells, while in the case of a purely electric field, no such shells are found for any value of $\sigma$.

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