92 research outputs found
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 is nonzero, (v)-(x)
two components of are nonzero, and (xi)-(xiv) three components of
are nonzero. Their relation with isometries of the space-times is
established. In case (v), when , 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 ,
or or . 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
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