On axially symmetric space–times admitting homothetic vector fields in Lyra’s geometry

Gad, Ragab M.; Mazrooei, A. E. Al

doi:10.1139/cjp-2016-0114

Cited by 2 publications

(2 citation statements)

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“…In addition to the above symmetry properties, different types of symmetries, such as isometry, homothetic, conformal, Ricci collineations, matter collineations, etc., are used to obtain exact solutions of Einstein's field equations. In the context of the theory of general relativity, these symmetries have been extensively studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Collinson and French [20], Katzin, Lavine and Davis [21], and Collinson [22] studied more general geometric symmetries.…”

Section: Introductionmentioning

confidence: 99%

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Self-Similar Solutions of a Bianchi Type-III Model with a Perfect Fluid and Cosmic String Cloud in Riemannian Geometry

Gad,

Al-Jedani

2023

Symmetry

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A Bianchi type-III cosmological model with self-similarity symmetry is investigated in cases with perfect fluid distribution and a cosmic string cloud. We show that this model admits a non-trivial homothetic vector field which possess non-null homothetic bivectors. This homothetic vector field is not parallel to its source vector (current vector). We discussed cases where the homothetic vector is either orthogonal or parallel to the 4-velocity of a fluid element. We solved Einstein’s field equations without making any assumptions on the geometry of space-time, only assuming that it admits self-similarity symmetry. We obtained new exact self-similar solutions for the Bianchi type-III model. We show that all obtained solutions are shear, and space-time is shear free in only the case where the homothetic vector field is parallel to the 4-velocity vector. The kinematical and physical properties of the obtained solutions are discussed.

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Section: Introductionmentioning

confidence: 99%

“…Self-similarity symmetry based on Lyra's geometry has been studied in [33][34][35][36][37]. The authors classified space-times according to admittance of such a symmetry.…”

Section: Introductionmentioning

confidence: 99%