Symmetries of the Energy-Momentum Tensor of Cylindrically Symmetric Static Spacetimes

TL;DR

This paper classifies matter symmetries in cylindrically symmetric static spacetimes, revealing the number of matter collineations varies with the degeneracy of the energy-momentum tensor and providing specific examples.

Contribution

It provides a comprehensive classification of matter symmetries for both degenerate and non-degenerate energy-momentum tensors in cylindrically symmetric static spacetimes.

Findings

Non-degenerate tensor yields 3, 4, 5, 6, 7, or 10 matter collineations.

Degenerate tensor can still have finite-dimensional symmetry groups, including 3, 4, 5, or 10 collineations.

Constructed examples satisfy energy-momentum tensor constraints.

Abstract

We investigate matter symmetries of cylindrically symmetric static spacetimes. These are classified for both cases when the energy-momentum tensor is non-degenerate and also when it is degenerate. It is found that the non-degenerate energy-momentum tensor gives either three, four, five, six, seven or ten independent matter collineations in which three are isometries and the rest are proper. The worth mentioning cases are those where we obtain the group of matter collineations finite-dimensional even the energy-momentum tensor is degenerate. These are either three, four, five or ten. Some examples are constructed satisfying the constraints on the energy-momentum tensor.