Killing Tensor of Five Dimensional Melvin’s Spacetime

Publication Issue: 
Volume 40, Issue 1, 2019
Page No: 
Date Received: 
Saturday, February 17, 2018
Authors' Name: 
Ganesh Subramaniam
Hishamuddin Zainuddin
Nurisya Mohd Shah
Authors' Affiliation and Address: 
Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research, University Putra Malaysia (UPM), 43400 UPM Serdang, Selangor.
Theoretical Physics Group, Department of Physics, Faculty of Science, University Putra Malaysia (UPM), 43400 UPM Serdang, Selangor.
Killing tensors are generalizations of Killing vectors as objects that reflect the symmetries of spacetime. With recent interest in higher-dimensional spacetimes, construction of Killing tensors from lower dimensional ones may be useful. Our focus lies in the (4+1) dimensional Melvin’s spacetime which describes a magnetic universe with a cylindrical symmetry. We constructed the Killing vectors and Killing tensors in 5-dimensional Melvin’s spacetime. The Killing tensors are a linear combination of scalar times a metric and respective symmetric product of Killing vectors similar to those found by Garfinkle and Glass for the 4-dimensional case. It is relatively easy to write down Killing tensors of a particular spacetime admitting both commuting and hypersurface orthogonal Killing vectors.
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