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.