Symmetries of the Energy–Momentum Tensor for Static Plane Symmetric Spacetimes
This article explores matter collineations (MCs) of static plane-symmetric spacetimes, considering the stress–energy tensor in its contravariant and mixed forms. We solve the MC equations in two cases: when the energy–momentum tensor is nondegenerate and degenerate. For the case of a degenerate ener...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/8/1614 |
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| author | Fawad Khan Wajid Ullah Tahir Hussain Wojciech Sumelka |
| author_facet | Fawad Khan Wajid Ullah Tahir Hussain Wojciech Sumelka |
| author_sort | Fawad Khan |
| collection | DOAJ |
| description | This article explores matter collineations (MCs) of static plane-symmetric spacetimes, considering the stress–energy tensor in its contravariant and mixed forms. We solve the MC equations in two cases: when the energy–momentum tensor is nondegenerate and degenerate. For the case of a degenerate energy–momentum tensor, we employ a direct integration technique to solve the MC equations, which leads to an infinite-dimensional Lie algebra. On the other hand, when considering the nondegenerate energy–momentum tensor, the contravariant form results in a finite-dimensional Lie algebra with dimensions of either 4 or 10. However, in the case of the mixed form of the energy–momentum tensor, the dimension of the Lie algebra is infinite. Moreover, the obtained MCs are compared with those already found for covariant stress–energy. |
| first_indexed | 2024-03-10T23:32:13Z |
| format | Article |
| id | doaj.art-012a7128cf954125bc5988de76c9d271 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T23:32:13Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-012a7128cf954125bc5988de76c9d2712023-11-19T03:12:16ZengMDPI AGSymmetry2073-89942023-08-01158161410.3390/sym15081614Symmetries of the Energy–Momentum Tensor for Static Plane Symmetric SpacetimesFawad Khan0Wajid Ullah1Tahir Hussain2Wojciech Sumelka3Department of Mathematics, University of Peshawar, Peshawar 25120, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25120, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25120, Khyber Pakhtunkhwa, PakistanInstitute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, PolandThis article explores matter collineations (MCs) of static plane-symmetric spacetimes, considering the stress–energy tensor in its contravariant and mixed forms. We solve the MC equations in two cases: when the energy–momentum tensor is nondegenerate and degenerate. For the case of a degenerate energy–momentum tensor, we employ a direct integration technique to solve the MC equations, which leads to an infinite-dimensional Lie algebra. On the other hand, when considering the nondegenerate energy–momentum tensor, the contravariant form results in a finite-dimensional Lie algebra with dimensions of either 4 or 10. However, in the case of the mixed form of the energy–momentum tensor, the dimension of the Lie algebra is infinite. Moreover, the obtained MCs are compared with those already found for covariant stress–energy.https://www.mdpi.com/2073-8994/15/8/1614matter collineationsstatic plane-symmetric spacetimescontravariant and mixed energy–momentum tensor |
| spellingShingle | Fawad Khan Wajid Ullah Tahir Hussain Wojciech Sumelka Symmetries of the Energy–Momentum Tensor for Static Plane Symmetric Spacetimes Symmetry matter collineations static plane-symmetric spacetimes contravariant and mixed energy–momentum tensor |
| title | Symmetries of the Energy–Momentum Tensor for Static Plane Symmetric Spacetimes |
| title_full | Symmetries of the Energy–Momentum Tensor for Static Plane Symmetric Spacetimes |
| title_fullStr | Symmetries of the Energy–Momentum Tensor for Static Plane Symmetric Spacetimes |
| title_full_unstemmed | Symmetries of the Energy–Momentum Tensor for Static Plane Symmetric Spacetimes |
| title_short | Symmetries of the Energy–Momentum Tensor for Static Plane Symmetric Spacetimes |
| title_sort | symmetries of the energy momentum tensor for static plane symmetric spacetimes |
| topic | matter collineations static plane-symmetric spacetimes contravariant and mixed energy–momentum tensor |
| url | https://www.mdpi.com/2073-8994/15/8/1614 |
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