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Algebraically special Einstein–Maxwell fields

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Abstract
The Geroch-Held-Penrose formalism is used to re-analyse algebraically special non-null Einstein-Maxwell fields, aligned as well as non-aligned, in the presence of a possible non-vanishing cosmological constant. A new invariant characterization is given of the Garc\'\i a-Pleba\'nski and Pleba\'nski-Hacyan metrics within the family of aligned solutions and of the Griffiths metrics within the family of the non-aligned solutions. As a corollary also the double alignment of the Debever-McLenaghan class $\mathcal{D}$' metrics with non-vanishing cosmological constant is shown to be equivalent with the shear-free and geodesic behavior of their Debever-Penrose vectors.
Keywords
Einstein-Maxwell, exact solutions, Goldberg-Sachs

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Citation

Chicago
Van den Bergh, Norbert. 2017. “Algebraically Special Einstein–Maxwell Fields.” Ed. Roy Maartens and Abhay Ashtekar. General Relativity and Gravitation 49 (1).
APA
Van den Bergh, N. (2017). Algebraically special Einstein–Maxwell fields. (R. Maartens & A. Ashtekar, Eds.)GENERAL RELATIVITY AND GRAVITATION, 49(1).
Vancouver
1.
Van den Bergh N. Algebraically special Einstein–Maxwell fields. Maartens R, Ashtekar A, editors. GENERAL RELATIVITY AND GRAVITATION. Springer; 2017;49(1).
MLA
Van den Bergh, Norbert. “Algebraically Special Einstein–Maxwell Fields.” Ed. Roy Maartens & Abhay Ashtekar. GENERAL RELATIVITY AND GRAVITATION 49.1 (2017): n. pag. Print.
@article{8514524,
abstract     = {The Geroch-Held-Penrose formalism is used to re-analyse algebraically special non-null Einstein-Maxwell fields, aligned as well as non-aligned, in the presence of a possible non-vanishing cosmological constant. A new invariant characterization is given of the Garc{\textbackslash}'{\textbackslash}i a-Pleba{\textbackslash}'nski and Pleba{\textbackslash}'nski-Hacyan metrics within the family of aligned solutions and of the Griffiths metrics within the family of the non-aligned solutions. As a corollary also the double alignment of the Debever-McLenaghan class \${\textbackslash}mathcal\{D\}\$' metrics with non-vanishing cosmological constant is shown to be equivalent with the shear-free and geodesic behavior of their Debever-Penrose vectors.},
author       = {Van den Bergh, Norbert},
editor       = {Maartens, Roy and Ashtekar, Abhay},
issn         = {0001-7701},
journal      = {GENERAL RELATIVITY AND GRAVITATION},
language     = {eng},
number       = {1},
publisher    = {Springer},
title        = {Algebraically special Einstein--Maxwell fields},
url          = {http://dx.doi.org/10.1007/s10714-016-2171-x},
volume       = {49},
year         = {2017},
}


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