Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-07-07
Class.Quant.Grav. 16 (1999) 2965-2985
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
24 pages, LaTeX2e, IOP style. To appear in Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/16/9/314
In this paper we study the electromagnetic fields generated by a Killing vector field in vacuum space-times (Papapetrou fields). The motivation of this work is to provide new tools for the resolution of Maxwell's equations as well as for the search, characterization, and study of exact solutions of Einstein's equations. The first part of this paper is devoted to an algebraic study in which we give an explicit and covariant procedure to construct the principal null directions of a Papapetrou field. In the second part, we focus on the main differential properties of the principal directions, studying when they are geodesic, and in that case we compute their associated optical scalars. With this information we get the conditions that a principal direction of the Papapetrou field must satisfy in order to be aligned with a multiple principal direction of the Weyl tensor in the case of algebraically special vacuum space-times. Finally, we illustrate this study using the Kerr, Kasner and pp waves space-times.
Fayos Francesc
Sopuerta Carlos F.
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