The Simon and Simon-Mars Tensors for Stationary Einstein-Maxwell Fields

Details The Simon and Simon-Mars Tensors for Stationary Einstein-Maxwell Fields The Simon and Simon-Mars Tensors for Stationary Einstein-Maxwell Fields

2004-03-04

arxiv.org/abs/gr-qc/0403022v1

Class.Quant.Grav. 21 (2004) 1987-1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, Latex IOP article class, no figures

Scientific paper

10.1088/0264-9381/21/8/005

Modulo conventional scale factors, the Simon and Simon-Mars tensors are defined for stationary vacuum spacetimes so that their equality follows from the Bianchi identities of the second kind. In the nonvacuum case one can absorb additional source terms into a redefinition of the Simon tensor so that this equality is maintained. Among the electrovacuum class of solutions of the Einstein-Maxwell equations, the expression for the Simon tensor in the Kerr-Newman-Taub-NUT spacetime in terms of the Ernst potential is formally the same as in the vacuum case (modulo a scale factor), and its vanishing guarantees the simultaneous alignment of the principal null directions of the Weyl tensor, the Papapetrou field associated with the timelike Killing vector field, the electromagnetic field of the spacetime and even the Killing-Yano tensor.

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