# Classification of LRS Bianchi type I Spacetimes via Conformal Ricci Collineations

## TL;DR

This paper classifies LRS Bianchi type I spacetimes based on their conformal Ricci collineations, revealing the dimensions of their symmetry algebras and providing examples with perfect fluid metrics.

## Contribution

It provides a complete classification of LRS Bianchi type I spacetimes according to their CRCs, including cases with degenerate and non-degenerate Ricci tensors.

## Key findings

- Spacetimes admit 7, 10, 11, or 15-dimensional CRC Lie algebras.
- Infinite CRCs occur when the Ricci tensor is degenerate.
- Examples of perfect fluid metrics with non-trivial CRCs are presented.

## Abstract

In this paper, we present a complete classification of Locally Rotationally Symmetric (LRS) Bianchi type I spacetimes according to their Conformal Ricci Collineations (CRCs). When the Ricci tensor is non-degenerate, a general form of the vector field generating CRCs is found, subject to some integrability conditions. Solving the integrability conditions in different cases, it is found that the LRS Bianchi type I spacetimes admit 7, 10, 11 or 15- dimensional Lie algebra of CRCs for the choice of non-degenerate Ricci tensor. Moreover, it is found that these spacetimes admit infinite number of CRCs when the Ricci tensor is degenerate. Some examples of perfect fluid LRS Bianchi type I spacetime metrics are provided admitting non trivial CRCs.