Classification of Spherically Symmetric Static Spacetimes According to Their Matter Collineations

Abstract

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 four, five, six, seven or ten independent matter collineations in which 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 four, six or ten.

Symmetries of Energy-Momentum Tensor: Some Basic Facts

“…Also, this may lead to problems related to the orbits of the resulting local diffeomorphism [7,12]. In the light of such problems and the usefulness of the covariant definition for MC [10,11] it can be concluded that the covariant definition of MC should be preferred.…”

“…There is a growing interest in the study of MCs [1,[8][9][10][11] and references therein]. Carot, et al [8] have discussed MCs from the point of view of the Lie algebra of vector fields generating them and, in particular, he discussed spacetimes with a degenerate T ab .…”

Geometrical/Physical Interpretation of the Conserved Quantities Corresponding to Noether Symmetries of Plane Symmetric Space-Times

“…In the past few decades, a significant amount of relativistic literature has been devoted to the study of symmetries in general relativity [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In [7], the authors considered Killing vectors (KVs) of spherically symmetric static space-times and concluded that they admit either ten KVs (corresponding to de Sitter, Minkowski, and anti-de Sitter metrics), seven KVs (corresponding to Einstein and anti-Einstein metrics), six KVs (incorporating the Bertotti-Robinson and two other metrics), or only four KVs (the minimal set of isometries).…”

Teleparallel Killing Vectors of the Einstein Universe

“…Camci and Sharif [15] worked out the MCs of homogeneous Gödel-type metrics. One of the authors (MS) [16][17] found the MCs of the spherically symmetric spacetimes (both static and non-static). Later, this work was extended to classify static plane and cylindrically symmetric spacetimes according to their MCs by the same author [18][19].…”