Conformal Ricci Collineations of Plane Symmetric Static Spacetimes

TL;DR

This paper investigates conformal Ricci collineations in plane-symmetric static spacetimes, solving the CRC equations and classifying the algebra's dimension, revealing finite and infinite dimensional cases.

Contribution

It provides a comprehensive analysis of CRCs in plane-symmetric static spacetimes, including explicit solutions and classification of the Lie algebra dimensions.

Findings

Finite-dimensional CRC algebra in non-degenerate case

Infinite-dimensional CRC algebra in degenerate case

Explicit spacetime metric solutions for certain degenerate cases

Abstract

This article explores the Conformal Ricci Collineations (CRCs) for the plane-symmetric static spacetime. The non-linear coupled CRC equations are solved to get the general form of conformal Ricci symmetries. In the non-degenerate case, it turns out that the dimension of the Lie algebra of CRCs is finite. In the case were the Ricci tensor is degenerate, it found that the algebra of CRCs for the plane-symmetric static spacetime is mostly, but not always, infinite dimensional. In one case of degenerate Ricci tensor, we solved the differential constraints completely and a spacetime metric is obtained along with CRCs. We found ten possible cases of finite and infinite dimensional Lie algebras of CRCs for the considered spacetime.