Energy conditions and conservation laws in LTB metric via Noether symmetries
Abstract In this paper, we have investigated Noether symmetries in Lemaitre–Tolman–Bondi (LTB) metric. Using the Lagrangian associated with the LTB metric, the set of determining equations for Noether symmetries is obtained and then integrated in several cases. It is shown that the LTB metric can be...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-08-01
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| Series: | European Physical Journal C: Particles and Fields |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-018-6164-7 |
| _version_ | 1818668379467153408 |
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| author | Tahir Hussain Sumaira Saleem Akhtar |
| author_facet | Tahir Hussain Sumaira Saleem Akhtar |
| author_sort | Tahir Hussain |
| collection | DOAJ |
| description | Abstract In this paper, we have investigated Noether symmetries in Lemaitre–Tolman–Bondi (LTB) metric. Using the Lagrangian associated with the LTB metric, the set of determining equations for Noether symmetries is obtained and then integrated in several cases. It is shown that the LTB metric can be classified in to eight distinct classes corresponding to Noether algebra of dimension 4, 5, 6, 7, 8, 9, 11 and 17. The obtained Noether symmetries are compared with Killing and homothetic vectors. The well known Noether’s theorem is used to find the expressions for conservation laws in each case. Moreover, it is shown that most of the obtained metrics are anisotropic or perfect fluid models which satisfy certain energy conditions and the equation of state. |
| first_indexed | 2024-12-17T06:35:23Z |
| format | Article |
| id | doaj.art-f41a89cf051943148748031eacf79473 |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-12-17T06:35:23Z |
| publishDate | 2018-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-f41a89cf051943148748031eacf794732022-12-21T22:00:01ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522018-08-017881910.1140/epjc/s10052-018-6164-7Energy conditions and conservation laws in LTB metric via Noether symmetriesTahir Hussain0Sumaira Saleem Akhtar1Department of Mathematics, University of PeshawarDepartment of Mathematics, University of PeshawarAbstract In this paper, we have investigated Noether symmetries in Lemaitre–Tolman–Bondi (LTB) metric. Using the Lagrangian associated with the LTB metric, the set of determining equations for Noether symmetries is obtained and then integrated in several cases. It is shown that the LTB metric can be classified in to eight distinct classes corresponding to Noether algebra of dimension 4, 5, 6, 7, 8, 9, 11 and 17. The obtained Noether symmetries are compared with Killing and homothetic vectors. The well known Noether’s theorem is used to find the expressions for conservation laws in each case. Moreover, it is shown that most of the obtained metrics are anisotropic or perfect fluid models which satisfy certain energy conditions and the equation of state.http://link.springer.com/article/10.1140/epjc/s10052-018-6164-7LTB metricNoether symmetryEnergy conditionsEquation of state |
| spellingShingle | Tahir Hussain Sumaira Saleem Akhtar Energy conditions and conservation laws in LTB metric via Noether symmetries European Physical Journal C: Particles and Fields LTB metric Noether symmetry Energy conditions Equation of state |
| title | Energy conditions and conservation laws in LTB metric via Noether symmetries |
| title_full | Energy conditions and conservation laws in LTB metric via Noether symmetries |
| title_fullStr | Energy conditions and conservation laws in LTB metric via Noether symmetries |
| title_full_unstemmed | Energy conditions and conservation laws in LTB metric via Noether symmetries |
| title_short | Energy conditions and conservation laws in LTB metric via Noether symmetries |
| title_sort | energy conditions and conservation laws in ltb metric via noether symmetries |
| topic | LTB metric Noether symmetry Energy conditions Equation of state |
| url | http://link.springer.com/article/10.1140/epjc/s10052-018-6164-7 |
| work_keys_str_mv | AT tahirhussain energyconditionsandconservationlawsinltbmetricvianoethersymmetries AT sumairasaleemakhtar energyconditionsandconservationlawsinltbmetricvianoethersymmetries |