We give a classification of the type D space–times based on the invariant differential properties of the Weyl principal structure. Our classification is established using tensorial invariants of the Weyl tensor and, consequently, besides its intrinsic nature, it is valid for the whole set of the type D metrics and it applies on both, vacuum and nonvacuum solutions. We consider the Cotton-zero type D metrics and we study the classes that are compatible with this condition. The subfamily of space–times with constant argument of the Weyl eigenvalue is analyzed in more detail by offering a canonical expression for the metric tensor and by giving a generalization of some results about the nonexistence of purely magnetic solutions. The usefulness of these results is illustrated in characterizing and classifying a family of Einstein–Maxwell solutions. Our approach permits us to give intrinsic and explicit conditions that label every metric, obtaining in this way an operational algorithm to detect them. In particular a characterization of the Reissner–Nordström metric is accomplished.
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February 2004
Research Article|
February 01 2004
On the classification of type D space–times Available to Purchase
Joan Josep Ferrando;
Joan Josep Ferrando
Departament d’Astronomia i Astrofı́sica, Universitat de València, E-46100 Burjassot, València, Spain
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Juan Antonio Sáez
Juan Antonio Sáez
Departament de Matemàtica Econòmico-Empresarial, Universitat de València, E-46071 València, Spain
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Joan Josep Ferrando
Departament d’Astronomia i Astrofı́sica, Universitat de València, E-46100 Burjassot, València, Spain
Juan Antonio Sáez
Departament de Matemàtica Econòmico-Empresarial, Universitat de València, E-46071 València, Spain
J. Math. Phys. 45, 652–667 (2004)
Article history
Received:
November 05 2002
Accepted:
November 12 2003
Citation
Joan Josep Ferrando, Juan Antonio Sáez; On the classification of type D space–times. J. Math. Phys. 1 February 2004; 45 (2): 652–667. https://doi.org/10.1063/1.1640795
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