Proper curvature collineations in non-static plane symmetric space-times

TL;DR

This paper investigates proper curvature collineations in non-static plane symmetric space-times, revealing they form an infinite dimensional vector space when such symmetries exist, using Riemann matrix rank and direct integration methods.

Contribution

It provides a detailed analysis of proper curvature collineations in non-static plane symmetric space-times, showing their infinite dimensionality under certain conditions.

Findings

Proper curvature collineations form an infinite dimensional vector space.

The study uses the rank of the Riemann matrix and direct integration techniques.

Conditions for the existence of proper curvature collineations are identified.

Abstract

The most general form of non-static plane symmetric space-times is considered to study proper curvature collineations by using the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper curvature collineations in each non static case of the above space-times it is shown that when the above space-times admit proper curvature collineations, they form an infinite dimensional vector space.