Proper Matter Collineations of Plane Symmetric Spacetimes (original) (raw)
Matter Collineations of Plane Symmetric Spacetimes
arXiv: General Relativity and Quantum Cosmology, 2008
This paper is devoted to the study of matter collineations of plane symmetric spacetimes (for a particular class of spacetimes) when the energy-momentum tensor is non-degenerate. There exists many interesting cases where we obtain proper matter collineations. The matter collineations in these cases are {\\it four}, \\emph{five}, {\\it six}, \\emph{seven} and {\\it ten} with some constraints on the energy-momentum tensor. We have solved some of these constraints to obtain solutions of the Einstein field equations.
Matter Symmetries of Non-Static Plane Symmetric Spacetimes
2020
The matter collineations of plane symmetric spacetimes are studied according to the degenerate energy-momentum tensor. We have found many cases where the energy-momentum tensor is degenerate but the group of matter collineations is finite. Further we obtain different constraint equations on the energy-momentum tensor. Solving these constraints may provide some new exact solutions of Einstein field equations.
Symmetries of the Energy-Momentum Tensor for Static Plane Symmetric Spacetimes
This article explores matter collineations (MCs) of static plane-symmetric spacetimes, considering the stress-energy tensor in its contravariant and mixed forms. We solve the MC equations in two cases: when the energy-momentum tensor is nondegenerate and degenerate. For the case of degenerate energy-momentum tensor, we employ a direct integration technique to solve the MC equations, which leads to an infinite-dimensional Lie algebra. On the other hand, when considering the nondegenerate energy-momentum tensor, the contravariant form results in a finite-dimensional Lie algebra with dimensions of either 4 or 10. However, in the case of the mixed form of the energy-momentum tensor, the dimension of the Lie algebra is infinite. Moreover, the obtained MCs are compared with those already found for covariant stress-energy.
Matter collineations of BKS-type spacetimes
Romanian Journal of Physics
In the present work, we classified the BKS-type (we refer to Bianchi-Kantowski-Sachs type spacetimes collectively as the BKS-type spacetimes) spacetimes (Bianchi type-V, Bianchi type-VI (m), Bianchi type-VII(m), Kantowski-Sachs) according to their matter collineations when the energy-momentum tensor is degenerate and also when it is non-degenerate. We find that the dimension of matter collineations is infinite and we have improper matter collineations for the degenerate case (there are seven possibilities make the energy-momentum tensor to be degenerate). Next, for the non-degenerate case of the energy-momentum tensor, we obtain proper matter collineations and find the dimension of the group is finite.
Classification of Spherically Symmetric Static Spacetimes According to Their Matter Collineations
General Relativity and Gravitation, 2003
The spherically symmetric static spacetimes are classified according to their matter collineations. These are studied when the energy-momentum tensor is degenerate and also when it is non-degenerate. We have found a case where the energy-momentum tensor is degenerate but the group of matter collineations is finite. For the non-degenerate case, we obtain either four, five, six or ten independent matter collineations in which four are isometries and the rest are proper. We conclude that the matter collineations coincide with the Ricci collineations but the constraint equations are different which on solving can provide physically interesting cosmological solutions.
Matter collineations of spacetime homogeneous G del-type metrics
Classical and Quantum Gravity, 2003
The spacetime homogeneous Gödel-type spacetimes which have four classes of metrics are studied according to their matter collineations. The obtained results are compared with Killing vectors and Ricci collineations. It is found that these spacetimes have infinite number of matter collineations in degenerate case, i.e. det(T ab ) = 0, and do not admit proper matter collineations in non-degenerate case, i.e. det(T ab ) = 0. The degenerate case has the new constraints on the parameters m and w which characterize the causality features of the Gödel-type spacetimes.
Matter collineations in Kantowski-Sachs, Bianchi types I and III spacetimes
2003
The matter collineation classifications of Kantowski-Sachs, Bianchi types I and III space times are studied according to their degenerate and non-degenerate energy-momentum tensor. When the energy-momentum tensor is degenerate, it is shown that the matter collineations are similar to the Ricci collineations with different constraint equations. Solving the constraint equations we obtain some cosmological models in this case. Interestingly, we have also found the case where the energy-momentum tensor is degenerate but the group of matter collineations is finite dimensional. When the energy-momentum tensor is non-degenerate, the group of matter collineations is finite-dimensional and they admit either four which coincides with isometry group or ten matter collineations in which four ones are isometries and the remaining ones are proper.
Symmetries of Energy-Momentum Tensor: Some Basic Facts
Communications in Theoretical Physics, 2007
It has been pointed by Hall et al. [1] that matter collinations can be defined by using three different methods. But there arises the question of whether one studies matter collineations by using the L ξ T ab = 0, or L ξ T ab = 0 or L ξ T b a = 0. These alternative conditions are, of course, not generally equivalent. This problem has been explored by applying these three definitions to general static spherically symmetric spacetimes. We compare the results with each definition.
Lie Symmetries of the Energy–Momentum Tensor for Plane Symmetric Static Spacetimes
International Journal of Modern Physics D, 2005
Matter collineations (MCs) are the vector fields along which the energy–momentum tensor remains invariant under Lie transport. Invariance of the metric, the Ricci and the Riemann tensors have been studied extensively and the vectors along which these tensors remain invariant are called Killing vectors (KVs), Ricci collineations (RCs) and curvature collineations (CCs), respectively. In this paper, plane symmetric static spacetimes have been studied for their MCs. Explicit form of MCs together with the Lie algebra admitted by them has been presented. Examples of spacetimes have been constructed for which MCs have been compared with their RCs and KVs. The comparison shows that neither of the sets of RCs and MCs contains the other, in general.
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.
Proper Curvature Collineations In Nonstatic Spherically Symmetric Space-Times
International …, 2008
We considered the special form of the non static axially symmetric space-times for studying proper curvature collineations by using the rank of the 6 × 6 Riemann matrix, direct integration and algebraic techniques. Studying proper curvature collineations in each case it is shown that when the above space-times admit proper curvature collineations, they form an infinite dimensional vector space. 2323 10 1 ( ( , , ) 2 ( , , )) ( , ,
Note on Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes
General Relativity and Gravitation, 2003
We show that the classification of Kantowski-Sachs, Bianchi Types I and III spacetimes admitting Matter Collineations (MCs) presented in a recent paper by Camci et al. [Camci, U., and Sharif, M. Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes, (2003) Gen. Relativ. Grav. 35 97-109] is incomplete. Furthermore for these spacetimes and when the Einstein tensor is nondegenerate, we give the complete Lie Algebra of MCs and the algebraic constraints on the spatial components of the Einstein tensor.
Matter collineation classification of Bianchi type II spacetime
General Relativity and Gravitation, 2006
In this paper we classified the matter collineations (MCs) of Bianchi type II spacetime according to the degenerate and non-degenerate energy-momentum tensor. It is shown that when the energy-momentum tensor is degenerate, most of the cases yield infinite dimensional MCs whereas some cases give finite dimensional Lie algebras in which there are three, four or five MCs. For the non-degenerate matter tensor cases we obtained that the Lie algebra of MCs is finite dimensional, in which the number of MCs are also three, four or five. Furthermore, we discussed the physical implications of the obtained MCs in the case of perfect fluid as source.
General Relativity and Gravitation, 2003
We show that the classification of Kantowski-Sachs, Bianchi Types I and III spacetimes admitting Matter Collineations (MCs) presented in a recent paper by Camci et al. [Camci, U., and Sharif, M. {Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes}, 2003 Gen. Relativ. Grav. vol. 35, 97-109] is incomplete. Furthermore for these spacetimes and when the Einstein tensor is non-degenerate, we give the complete Lie Algebra of MCs and the algebraic constraints on the spatial components of the Einstein tensor.
Proper Curvature Collineations In Non-Static Plane Symmetric Space-Times
depmath.ulbsibiu.ro
The most general form of non-static plane symmetric space-times is considered to study proper curvature collineations by using the rank of the 6 × 6 Riemann matrix and direct integration techniques. Studying proper curvature collineations in each non static case of the above ...
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.
Comment: Note on Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes
General Relativity and Gravitation, 2003
We show that the classification of Kantowski-Sachs, Bianchi Types I and III spacetimes admitting Matter Collineations (MCs) presented in a recent paper by Camci et al. [Camci, U., and Sharif, M. Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes, (2003) Gen. Rel. Grav. 35, 97-109.] is incomplete. Furthermore for these spacetimes and when the Einstein tensor is non-degenerate, we give the complete Lie Algebra of MCs and the algebraic constraints on the spatial components of the Einstein tensor.
Spacetimes with Pseudosymmetric Energy-momentum Tensor
Communications in Physics, 2016
The object of the present paper is to introduce spacetimes with pseudosymmetricenergy-momentum tensor. In this paper at first we consider the relation \(R(X,Y)\cdot T=fQ(g,T)\), that is, the energy-momentumtensor \(T\) of type (0,2) is pseudosymmetric. It is shown that in a general relativistic spacetimeif the energy-momentum tensor is pseudosymmetric, then the spacetime is also Ricci pseudosymmetricand the converse is also true. Next we characterize the perfect fluid spacetimewith pseudosymmetric energy-momentum tensor. Finally, we consider conformally flat spacetime withpseudosymmetric energy-momentum tensor.
Matter collineations: The inverse ‘‘symmetry inheritance’’ problem
Journal of Mathematical Physics, 1994
Matter collineations, as a symmetry property of the energy-momentum tensor Tab, are studied from the point of view of the Lie algebra of vector fields generating them. Most attention is given to space-times with a degenerate energy-momentum tensor. Some examples of matter collineations are found for dust fluids (including Szekeres's space-times), and null fluid space-times.