Abstract
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.
Highlights
Collineations are the geometric assumptions which concern the “symmetries” of the metric defined by the Lie symmetries of either the metric itself or the tensors defined from the metric [1,2]
Due to high non linearity, it is very difficult to find the exact solutions of the system. To overcome this difficulty we introduce symmetry
MCs are totally related to the physical properties of the spacetimes, whereas RCs are concerned with the geometry of spacetimes [2,5].There are many approaches to discuss RCs and MCs but the technique used to find RCs and MCs is vanishing Lie derivative of RICCI and energy momentum tensors along with the specified vector fields [6]
Summary
Collineations are the geometric assumptions which concern the “symmetries” of the metric defined by the Lie symmetries of either the metric itself or the tensors defined from the metric [1,2]. The left hand side of EFEs describes the geometry while the RHS is totally related to physics In these equations, Λ is called cosmological constant and κ = 8πG/C4 is called coupling constant [3]. Analysis of Optical Attenuation from Measured Visibility Data in Islamabad, Pakistan restrictions These symmetry restrictions for mechanical problems reduce the degrees of freedom. It is obvious from the EFEs that RICCI and matter collineations are necessary to find the exact solutions of EFEs. MCs are totally related to the physical properties of the spacetimes, whereas RCs are concerned with the geometry of spacetimes [2,5].There are many approaches to discuss RCs and MCs but the technique used to find RCs and MCs is vanishing Lie derivative of RICCI and energy momentum tensors along with the specified vector fields [6]. Semicolon and L are the symbols used for partial, covariant and Lie derivatives respectively [5]
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