Symmetries of the Energy-Momentum Tensor: Some Basic Facts

Abstract

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 ${\mathcal{L}}_{\xi }{T}_{ab}=0$, or ${\mathcal{L}}_{\xi }{T}^{ab}=0$ or ${\mathcal{L}}_{\xi }{T}_a^b=0$. 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.

arXiv comment17 pages, accepted for publication in "Communications in Theoretical Physics"

References in corpus (5)

• Matter collineations of Spacetime Homogeneous Gödel-type Metrics
• Classification of Static Plane Symmetric Spacetimes according to their Matter Collineations
• Symmetries of the Energy-Momentum Tensor of Cylindrically Symmetric Static Spacetimes
• Symmetries of the Energy-Momentum Tensor of Spherically Symmetric Lorentzian Manifolds
• Classification of Spherically Symmetric Static Spacetimes according to their Matter Collineations