Teleparallel Conformal Killing Vector Fields of LRS Bianchi Type V Spacetimes in Teleparallel Gravity

TL;DR

This paper investigates the properties of conformal Killing vector fields in LRS Bianchi type V spacetimes within teleparallel gravity, revealing conditions under which proper vector fields exist and comparing these with general relativity results.

Contribution

It provides the first detailed analysis of teleparallel conformal Killing vector fields in LRS Bianchi type V spacetimes, highlighting differences from general relativity.

Findings

Proper teleparallel CKVFs exist only in specific cases.

Most cases reduce to teleparallel KVFs.

No proper teleparallel HVFs are admitted.

Abstract

The aim of this paper is to explore teleparallel conformal Killing vector fields (CKVFs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes in the context of teleparallel gravity and compare the obtained results with those of general relativity. The general solution of teleparallel conformal Killing's equations is found in terms of some unknown functions of t and x , along with a set of integrability conditions. The integrability conditions are solved in some particular cases to get the final form of teleparallel CKVFs. It is observed that the LRS Bianchi type V spacetimes admit proper teleparallel CKVF in only one case, while in remaining cases the teleparallel CKVFs reduce to teleparallel Killing vector fields (KVFs). Moreover, it is shown that the LRS Bianchi type V spacetimes do not admit any proper teleparallel homothetic vector field (HVF).