Conformal Collineations of the Ricci and Energy-Momentum Tensors in Static Plane Symmetric Spacetimes

TL;DR

This paper classifies static plane symmetric spacetimes based on conformal Ricci and matter collineations, revealing the dimensions of their Lie algebras and exploring physical implications with perfect fluid sources.

Contribution

It provides a complete classification of static plane symmetric spacetimes according to conformal Ricci and matter collineations, including new forms of vector fields and metric solutions.

Findings

Spacetimes have 7, 10, or 15-dimensional Lie algebras of CRCs.

Infinite CRCs occur when the Ricci tensor is degenerate.

Exact metrics admitting non-trivial CRCs and CMCs are derived.

Abstract

Considering the degenerate and non-degenerate cases, we provide a complete classification of static plane symmetric spacetimes according to conformal Ricci collineations (CRCs) and conformal matter collineations (CMCs). In case of non-degenerate Ricci tensor, a general form of vector field generating CRCs is found in terms of unknown functions of t and x, subject to some integrability conditions. The integrability conditions are then solved in different cases depending upon the nature of Ricci tensor and it is concluded that static plane symmetric spacetimes possess 7, 10 or 15-dimensional Lie algebra of CRCs. Moreover, it is found that these spacetimes admit infinite number of CRCs when the Ricci tensor is degenerate. A similar procedure is adopted for the study of CMCs in degenerate and non-degenerate matter tensor cases. The exact form of some static plane symmetric spacetimes metrics is obtained admitting non-trivial CRCs and CMCs. Finally, we present some physical implications of our obtained results by considering a perfect fluid as a source of the energy-momentum tensor.