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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| Format: | Thesis |
| Language: | English |
| Published: |
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/84992/1/IPM%202019%2020%20-%20ir.pdf |
| _version_ | 1825952033015857152 |
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| author | Subramaniam, Ganesh |
| author_facet | Subramaniam, Ganesh |
| author_sort | Subramaniam, Ganesh |
| collection | UPM |
| description | 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. |
| first_indexed | 2024-03-06T10:38:56Z |
| format | Thesis |
| id | upm.eprints-84992 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T10:38:56Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | upm.eprints-849922021-12-31T02:40:02Z http://psasir.upm.edu.my/id/eprint/84992/ Killing tensor of five dimensional Melvin’s spacetime Subramaniam, Ganesh 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. 2018-02 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/84992/1/IPM%202019%2020%20-%20ir.pdf Subramaniam, Ganesh (2018) Killing tensor of five dimensional Melvin’s spacetime. Masters thesis, Universiti Putra Malaysia. Calculus of tensors Space and time Geometrodynamics |
| spellingShingle | Calculus of tensors Space and time Geometrodynamics Subramaniam, Ganesh Killing tensor of five dimensional Melvin’s spacetime |
| title | Killing tensor of five dimensional Melvin’s spacetime |
| title_full | Killing tensor of five dimensional Melvin’s spacetime |
| title_fullStr | Killing tensor of five dimensional Melvin’s spacetime |
| title_full_unstemmed | Killing tensor of five dimensional Melvin’s spacetime |
| title_short | Killing tensor of five dimensional Melvin’s spacetime |
| title_sort | killing tensor of five dimensional melvin s spacetime |
| topic | Calculus of tensors Space and time Geometrodynamics |
| url | http://psasir.upm.edu.my/id/eprint/84992/1/IPM%202019%2020%20-%20ir.pdf |
| work_keys_str_mv | AT subramaniamganesh killingtensoroffivedimensionalmelvinsspacetime |