Conformal Collineations in String Cosmology

Baysal, Hüsnü; Camcı, Uğur; Tarhan, İsmail; Yılmaz, İhsan; Yavuz, Ilhami

doi:10.1142/s0218271802001755

Cited by 16 publications

(10 citation statements)

References 7 publications

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“…For a(x i ) = 0 they reduce to the Ricci collineations (RC) which have been considered many times in the literature. RICs for string fluids generated by the spacelike vector ξ a = ξ n a have been considered before in [9] however,as we shall show, in an incomplete way. RCs for string fluid have been considered in [7].…”

Section: The Ricci Inheritance Collineations For a String Fluidmentioning

confidence: 98%

“…7 The case of a spacelike conformal Killing vector ξ a = ξ n a [6,9] The case of a spacelike CKV ξ a = ξ n a is studied in a similar manner as the one of the timelike CKV ξ a = ξ u a . Relation (90) still holds but now the difference is that L ξ R ab for a string fluid is given by (35) and the kinematic conditions by relations (80) to (83).…”

Section: Propositionmentioning

confidence: 99%

See 1 more Smart Citation

General symmetries of a string fluid space-time

Tsamparlis

2006

Gen Relativ Gravit

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It is shown that a string fluid is the simplest anisotropic fluid with vanishing heat flux. Furthermore it has the property that the Ricci tensor is obtained from the energy momentum tensor, and vice versa, if one interchanges the fluid variables. We use previous works on the collineations of anisotropic fluids, which include the string fluid as a particular case, to compute the kinematic and the dynamic effects of certain collineations of a string fluid. It is found that the possible spacetimes, which can carry a string fluid, are severely restricted and the possible string fluids in spacetimes, which can admit them are more or less fixed. We recover previous results on the effect of symmetries in string fluid spacetimes and get many new ones, for example the matter inheritance collineations. The study and the results are presented in a systematic manner, which allows the comprehension and the comparison of the restrictions imposed by each collineation. Finally one can use the same method of work for a systematic study of similar problems.

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Section: The Ricci Inheritance Collineations For a String Fluidmentioning

confidence: 98%

Section: Propositionmentioning

confidence: 99%

General symmetries of a string fluid space-time

Tsamparlis

2006

Gen Relativ Gravit

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“…One direction in which the string fluids have been studied is the simplification of the field equations for various types of collineations of spacetime [15], [16], [18], [17], [19], [20] [29]. In the next sections we extend these studies to the case of the EMSF.…”

Section: The Electromagnetic String Fluid (Emsf)mentioning

confidence: 99%

Symmetries of spacetimes embedded with an electromagnetic string fluid

Tsamparlis¹,

Mitsopoulos²,

Paliathanasis³

2018

Gen Relativ Gravit

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The electromagnetic string fluid (EMSF) is an anisotropic charged string fluid interacting with a strong magnetic field. In this fluid we consider the double congruence defined by the 4-velocity of the fluid u a and the unit vector n a along the magnetic field. Using the standard 1+3 decomposition defined by the vector u a and the 1+1+2 decomposition defined by the double congruence u a , n a we determine the kinematic and the dynamic quantities of an EM string fluid in both decompositions. In order to solve the resulting field equations we consider simplifying assumptions in the form of collineations. We decompose the generic quantity LX g ab in a trace ψ and and a traceless part H ab . Because all collineations are expressible in terms of the quantity LX g ab it is possible to compute the Lie derivative of all tensors defined by the metric i.e. the Ricci tensor, the Weyl tensor etc. This makes possible the effects of any assumed collineation on the gravitational field equations. This is done as follows. Using relevant identities of Differential Geometry we express the quantity LX R ab where R ab is the Ricci tensor in terms of the two irreducible parts ψ, H ab . Subsequently using the gravitational field equations we compute the same quantity LX R ab in terms of the Lie derivative of the dynamic variables. We equate the two results and find the field equations in the form LX Dynamic variable = F (ψ, H ab , dynamic variables). This result is general and holds for all gravitational systems and in particular for the EMSF. Subsequently we specialize our study at two levels. We consider the case of a Conformal Killing Vector (CKV) parallel to u a and a CKV parallel to n a . Finally we solve the resulting field equations in the first case to the Friedman Robertson Walker (FRW) spacetime and in the second case for the Bianchi I spacetime. In the latter case we find a new solution of the gravitational field equations. *

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“…Mason and Maartens [19] discussed the kinematic properties of anisotropic fluids admitting conformal collineations. The spacelike CRCs in models of a string cloud and string fluid stress tensor are investigated by Baysal et al [1]. The spacelike CKVs in a spacelike congruence were studied by Mason and Tsamparlis [20].…”

Section: Introductionmentioning

confidence: 99%

Non-static spherically symmetric spacetimes and their conformal Ricci collineations

et al. 2019

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For a perfect fluid matter, we present a study of conformal Ricci collineations (CRCs) of non-static spherically symmetric spacetimes. For non-degenerate Ricci tenor, a vector field generating CRCs is found subject to certain integrability conditions. These conditions are then solved in various cases by imposing certain restrictions on the Ricci tensor components. It is found that non-static spherically symmetric spacetimes admit 5, 6 or 15 CRCs. In the degenerate case, it is concluded that such spacetimes always admit infinite number of CRCs.

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Conformal Collineations in String Cosmology

Cited by 16 publications

References 7 publications

General symmetries of a string fluid space-time

General symmetries of a string fluid space-time

Symmetries of spacetimes embedded with an electromagnetic string fluid

Non-static spherically symmetric spacetimes and their conformal Ricci collineations

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