Killing vector fields of locally rotationally symmetric Bianchi type V spacetime

Shakeel Ahmad; Tahir Hussain; Abdul Baseer Saqib; Muhammad Farhan; Muhammad Farooq

doi:10.1038/s41598-024-58560-3

Killing vector fields of locally rotationally symmetric Bianchi type V spacetime

Sci Rep. 2024 May 3;14(1):10239. doi: 10.1038/s41598-024-58560-3.

Authors

Shakeel Ahmad¹, Tahir Hussain², Abdul Baseer Saqib³, Muhammad Farhan², Muhammad Farooq²

Affiliations

¹ Department of Basic Science and Humanities, CECOS University, Peshawar, Khyber Pakhtunkhwa, Pakistan.
² Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan.
³ Faculty of Education, Nangrahar University, Jalalabad, Nangrahar, Afghanistan. ab_saqib@nu.edu.af.

Abstract

The classification of locally rotationally symmetric Bianchi type V spacetime based on its killing vector fields is presented in this paper using an algebraic method. In this approach, a Maple algorithm is employed to transform the Killing's equations into a reduced evolutive form. Subsequently, the integration of the Killing's equations is carried out subject to the constraints provided by the algorithm. The algorithm demonstrates that there exist fifteen distinct metrics that could potentially possess Killing vector fields. Upon solving the Killing equations for all fifteen metrics, it is observed that seven out of the fifteen metrics exclusively exhibit the minimum number of Killing vector fields. The remaining eight metrics admit a varying number of Killing vector fields, specifically 6, 7, or 10. The Kretschmann scalar has been computed for each of the obtained metrics, revealing that all of them possess a finite Kretschmann scalar and thus exhibit regular behavior.

Keywords: Killing symmetry; Kretschmann scalar; LRS Bianchi type V metric; Rif tree approach.