Towards a Complete Classification of Spherically Symmetric Lorentzian Manifolds According to Their Ricci Collineations

M. Ziad*

*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلةReview articleمراجعة النظراء

12 اقتباسات (Scopus)

ملخص

General expressions for the components of the Ricci collineation vector are derived and the related constraints are obtained. These constraints are then solved to obtain Ricci collineations and the related constraints on the Ricci tensor components for all spacetime manifolds (degenerate or non-degenerate, diagonal or non-diagonal) admitting symmetries larger than so(3) and already known results are recovered. A complete solution is achieved for the spacetime manifolds admitting so(3) as the maximal symmetry group with non-degenerate and non diagonal Ricci tensor components. It is interesting to point out that there appear cases with finite number of Ricci collineations although the Ricci tensor is degenerate and also the cases with infinitely many Ricci collineations even in the case of non-degenerate Ricci tensor. Interestingly, it is found that the spacetime manifolds with so(3) as maximal symmetry group may admit two extra proper Ricci collineations, although they do not admit a G5 as the maximal symmetry group. Examples are provided which show and clarify some comments made by Camci et al. [Camci, U., and Branes, A. (2002). Class. Quantum Grav. 19, 393-404]. Theorems are proved which correct the earlier claims made in [Carot, J., Nunez, L. A., and Percoco, U. (1997). Gen. Relutiv. Gravit. 29, 1223-1237; Contreras, G., Núñez, L. A., and Percolo, U. (2000). Gen. Relativ. Gravit. 32, 285-294].

اللغة الأصليةEnglish
الصفحات (من إلى)915-936
عدد الصفحات22
دوريةGeneral Relativity and Gravitation
مستوى الصوت35
رقم الإصدار5
المعرِّفات الرقمية للأشياء
حالة النشرPublished - مايو 2003
منشور خارجيًانعم

ASJC Scopus subject areas

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