Concircular vector fields for Kantowski–Sachs and Bianchi type-III spacetimes

Author:

Khan Suhail1,Mahmood Amjad1,Ali Ahmad T.23

Affiliation:

1. Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtoonkhwa, Pakistan

2. King Abdulaziz University, Faculty of Science, Department of Mathematics, P.O. Box 80203, Jeddah 21589, Saudi Arabia

3. Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, 11884 Cairo, Egypt

Abstract

This paper intends to obtain concircular vector fields (CVFs) 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 (CKVFs) 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

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1. Perfect fluid locally rotationally symmetric Bianchi Type-I spacetimes admitting concircular vector fields in f(T) gravity;International Journal of Geometric Methods in Modern Physics;2024-04-13

2. Ricci Soliton Lightlike Submanifolds with Co-Dimension $2$;Fundamental Journal of Mathematics and Applications;2023-06-30

3. A note on concircular vector fields of static plane symmetric perfect fluid spacetimes in f(T) theory of gravity;The European Physical Journal Plus;2023-06-15

4. Ricci soliton vector fields of Kantowski–Sachs spacetimes;Modern Physics Letters A;2022-07-20

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