Killing tensor of five dimensional Melvin’s spacetime
In this research, (3+1)D Melvin’s spacetime was extended into (4+1)D Melvin’s spacetime using hypersphere coordinates. Later, the method to compute Killing ten- sor as introduced by Garfinkle for (3+1)D spacetime was studied to compute Killing tensor in (4+1)D Melvin’s spacetime. Th...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
2018
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/84992/1/IPM%202019%2020%20-%20ir.pdf |
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| Summary: | In this research, (3+1)D Melvin’s spacetime was extended into (4+1)D Melvin’s spacetime
using hypersphere coordinates. Later, the method to compute Killing ten- sor as introduced by
Garfinkle for (3+1)D spacetime was studied to compute Killing tensor in (4+1)D Melvin’s spacetime.
The method introduced by Garfinkle needs the existence of commuting Killing vectors or Killing
vectors in a particular coor- dinate direction. It is not well understood that the method
introduced by Garfinkle worked well for extended (4+1)D Melvin’s metric because the fifth component
of the metric canceled one of the commuting Killing vector in 3-dimension. Therefore, Killing
tensors are obtained using the method introduced by Garfinkle and they are compared with the ones
obtained by symmetrically multiplying the Killing vectors. For the later case, we found Killing
vectors and Killing tensors for (4+1)D Melvin’s spacetime. At the end it is concluded that the
Killing tensor found for (4+1)D con- sist of products of some noncommuting Killing vector. Killing
tensor found in this research might be applicable in separability of Hamilton-Jacobi and
Klein-Gordon
equation. |
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