Concircular vector fields for Kantowski Sachs and Bianchi type III spacetimes

TL;DR

This paper derives concircular vector fields for Kantowski Sachs and Bianchi type III spacetimes, revealing their symmetry structures and restrictions on metric functions, with implications for Einstein spaces and conformal Ricci collineations.

Contribution

It provides the first detailed derivation of concircular vector fields for these spacetimes, including conditions and classifications based on symmetry dimensions.

Findings

Spacetimes admit 4, 6, or 15 dimensional concircular vector fields.

In Einstein spaces, all conformal Killing vectors are concircular.

Concircular vector fields are also conformal Ricci collineations.

Abstract

This paper intends to obtain concircular vector fields of Kantowski Sachs and Bianch type III spacetimes. For this purpose, ten conformal Killing equations and their general solution in the form of conformal Killing vector fields are derived along with their conformal factors. The obtained conformal Killing vector fields are then placed in Hessian equations to obtain the final form of concircular vector fields. The existence of concircular symmetry imposes restrictions on the metric functions. The conditions imposing restrictions on these metric functions are obtained as a set of integrability conditions. It is shown that Kantowski Sachs and Bianchi type III spacetimes admit four, six, or fifteen dimensional concircular vector fields. It is established that for Einstein spaces, every conformal Killing vector field is a concircular vector field. Moreover, it is explored that every concircular vector field obtained here is also a conformal Ricci collineation.