Curvature Inheritance Symmetry In Riemannian Spaces with Applications to String Cloud and String Fluids

TL;DR

This paper investigates curvature inheritance symmetries in Riemannian spaces with applications to string cloud and string fluids within general relativity, revealing conditions under which these symmetries relate to conformal Killing vectors.

Contribution

It introduces the concept of curvature inheritance symmetry for string cloud and string fluid models, exploring their properties and connections to conformal Killing vectors in a relativistic context.

Findings

Derived conditions for curvature inheritance symmetry in string cloud and string fluid models

Established relationship between proper CI and conformal Killing vectors

Provided new insights into symmetry properties in general relativistic string models

Abstract

We study, in this paper, curvature inheritance symmetry (CI), $\pounds_{\xi}R_{bcd}^{a}=2\alpha R_{bcd}^{a}$, where $\alpha $ is a scalar function, for string cloud and string fluid in the context of general relativity. Also, we have obtained some result when a proper CI (i.e., $\alpha \neq 0$) is also a conformal Killing vector.