Ricci Collineations for Non-degenerate, Diagonal and Spherically Symmetric Ricci Tensors (original) (raw)
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Comment on Ricci Collineations for spherically symmetric space-times
General Relativity and Gravitation, 2002
It is shown that the results of the paper by Contreras et al. [Contreras, G., Nunez, L. A., Percoco, U. Ricci Collineations for Non-degenerate, Diagonal and Spherically Symmetric Ricci Tensors . Gen. Rel. Grav. 32, 285-294] concerning the Ricci Collineations in spherically symmetric spacetimes with non-degenerate and diagonal Ricci tensor do not cover all possible cases. Furthermore the complete algebra of Ricci Collineations of certain Robertson-Walker metrics of vanishing spatial curvature are given.
Letter: Comment on Ricci Collineations for Spherically Symmetric Space-Times
Gen Relativ Gravit, 2002
It is shown that the results of the paper by Contreras et al. [Contreras, G., Nunez, L. A., Percoco, U. Ricci Collineations for Non-degenerate, Diagonal and Spherically Symmetric Ricci Tensors . Gen. Rel. Grav. 32, 285-294] concerning the Ricci Collineations in spherically symmetric spacetimes with non-degenerate and diagonal Ricci tensor do not cover all possible cases. Furthermore the complete algebra of Ricci Collineations of certain Robertson-Walker metrics of vanishing spatial curvature are given.
Ricci Tensors with Rotational Symmetry on R^n
In this paper is considered the differential equation Ric(g) = T , where Ric(g) is the Ricci tensor of the metric g and T is a rotational symmetric tensor on R n. A new, geometric, proof of the existence of smooth solutions of this equation, based on qualitative theory of implicit differential equations, is presented here. This result was obtained previously by DeTurck and Cao in 1994.
Ricci and matter collineations of locally rotationally symmetric space-times
A new method is presented for the determination of Ricci Collineations (RC) and Matter Collineations (MC) of a given spacetime, in the cases where the Ricci tensor and the energy momentum tensor are non-degenerate and have a similar form with the metric. This method reduces the problem of finding the RCs and the MCs to that of determining the KVs whereas at the same time uses already known results on the motions of the metric. We employ this method to determine all hypersurface homogeneous locally rotationally symmetric spacetimes, which admit proper RCs and MCs. We also give the corresponding collineation vectors.
Theoretical and Mathematical Physics, 2018
Considering the degenerate and non-degenerate cases, we provide a complete classification of static plane symmetric spacetimes according to conformal Ricci collineations (CRCs) and conformal matter collineations (CMCs). In case of non-degenerate Ricci tensor, a general form of vector field generating CRCs is found in terms of unknown functions of t and x, subject to some integrability conditions. The integrability conditions are then solved in different cases depending upon the nature of Ricci tensor and it is concluded that static plane symmetric spacetimes possess 7, 10 or 15-dimensional Lie algebra of CRCs. Moreover, it is found that these spacetimes admit infinite number of CRCs when the Ricci tensor is degenerate. A similar procedure is adopted for the study of CMCs in degenerate and non-degenerate matter tensor cases. The exact form of some static plane symmetric spacetimes metrics is obtained admitting non-trivial CRCs and CMCs. Finally, we present some physical implications of our obtained results by considering a perfect fluid as a source of the energy-momentum tensor.
Ricci Collineations of Static Space Times with Maximal Symmetric Transverse Spaces
Communications in Theoretical Physics, 2006
Static space times with maximal symmetric transverse spaces are classified according to their Ricci collineations. These are investigated for non-degenerate Ricci tensor (det.(R α) = 0). It turns out that the only collineations admitted by these spaces can be ten, seven, six or four. Some new metrics admitting proper Ricci collineations are also investigated.
RICCI and Matter Collineations of SOM-ROY Chaudhary Symmetric Space Time
Mehran University Research Journal of Engineering and Technology
This paper is devoted to explore the RICCI and MCs (Matter Collineations of the Som-Ray Chaudhary spacetime. The spacetime under consideration is one of the spatially homogeneous and rotating spacetimes. Collineations are the some kinds of the Lie symmetries. To discuss the required collineations we have used the RICCI and energy momentum tensors. As the RICCI tensor is formulated from the metric tensor, it must possess its symmetries. RCs (RICCI Collineations) leads to conservation laws. On the other hand for the distribution of matter in the spacetimes, the symmetries of energy momentum tensor or MCs provides conservation laws on matter field. Throughout this paper, these collineations are discussed by vanishing Lie derivative of RICCI and energy momentum tensors respectively. Complete solution of the RCs and MCs equations, which are formed in the result of vanishing Lie derivative are explored. Studying all these collineations in the said spacetime, it has been shown that RCs of the spacetime form an infinite dimensional vector space where as MCs are Killing vector fields.