Approximate Noether gauge symmetries of Bardeen model

We investigate the approximate Noether gauge symmetries of the geodesic Lagrangian for the Bardeen spacetime model. This is accommodated by a set of new approximate Noether gauge symmetry relations for the perturbed geodesic Lagrangian in the spacetime. A detailed analysis to the spacetime of Bardeen model up to third-order approximate Noether gauge symmetries is presented.Comment: 7 pages, 1 table, submitted to the EPJ

Classification of Static Plane Symmetric Spacetimes according to their Matter Collineations

In this paper we classify static plane symmetric spacetimes according to their matter collineations. These have been studied for both cases when the energy-momentum tensor is non-degenerate and also when it is degenerate. It turns out that the non-degenerate case yields either {\it four}, {\it five}, {\it six}, {\it seven} or {\it ten} independent matter collineations in which {\it four} are isometries and the rest are proper. There exists three interesting cases where the energy-momentum tensor is degenerate but the group of matter collineations is finite-dimensional. The matter collineations in these cases are either {\it four}, {\it six} or {\it tenComment: 15 pages, LaTex, no figure

Classification of Spherically Symmetric Static Spacetimes according to their Matter Collineations

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 {\it four}, {\it five}, {\it six} or {\it 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.Comment: 15 pages, no figure, Late

Ricci Collineations of the Bianchi Types I and III, and Kantowski-Sachs Spacetimes

Ricci collineations of the Bianchi types I and III, and Kantowski-Sachs space- times are classified according to their Ricci collineation vector (RCV) field of the form (i)-(iv) one component of $\xi^a (x^b)$ is nonzero, (v)-(x) two components of $\xi^a (x^b)$ are nonzero, and (xi)-(xiv) three components of $\xi^a (x^b)$ are nonzero. Their relation with isometries of the space-times is established. In case (v), when $det(R_{ab}) = 0$, some metrics are found under the time transformation, in which some of these metrics are known, and the other ones new. Finally, the family of contracted Ricci collineations (CRC) are presented.Comment: 21 Pages, LaTeX, no figures, accepted for publication in the International Journal of Modern Physics

Note on Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes

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.Comment: 10 pages, Latex. Accepted for publication in General Relativity and Gravitatio

Conformal Ricci collineations of static spherically symmetric spacetimes

Conformal Ricci collineations of static spherically symmetric spacetimes are studied. The general form of the vector fields generating conformal Ricci collineations is found when the Ricci tensor is non-degenerate, in which case the number of independent conformal Ricci collineations is \emph{fifteen}; the maximum number for 4-dimensional manifolds. In the degenerate case it is found that the static spherically symmetric spacetimes always have an infinite number of conformal Ricci collineations. Some examples are provided which admit non-trivial conformal Ricci collineations, and perfect fluid source of the matter

Symmetries of the Energy-Momentum Tensor: Some Basic Facts

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 ${\cal L}_\xi T_{ab}=0$, or ${\cal L}_\xi T^{ab}=0$ or ${\cal L}_\xi T_a^b=0$. 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.Comment: 17 pages, accepted for publication in "Communications in Theoretical Physics