A note on the equivalence of energy–momentum distribution for diagonal and non-diagonal models in general relativity and teleparallel gravity
In this paper, it is shown that the super-potential defined by Einstein, Landau–Lifshitz, and Bergmann–Thompson in general relativity theory and in teleparallel gravity theory are equivalent for a general diagonal space–time metric. Therefore, the energy–momentum tensor defined by Einstein, Landau–L...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-09-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722004545 |
| _version_ | 1817995495161724928 |
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| author | Ahmad T. Ali |
| author_facet | Ahmad T. Ali |
| author_sort | Ahmad T. Ali |
| collection | DOAJ |
| description | In this paper, it is shown that the super-potential defined by Einstein, Landau–Lifshitz, and Bergmann–Thompson in general relativity theory and in teleparallel gravity theory are equivalent for a general diagonal space–time metric. Therefore, the energy–momentum tensor defined by Einstein, Landau–Lifshitz, and Bergmann–Thompson is equivalent in general relativity theory and in teleparallel gravity theory for the general diagonal space–times. Two different examples are also given to ensure the validity of the established statements. However, this fact is not true in general for the non-diagonal space–times. Non-diagonal Phantom black hole metric and non-diagonal stationary axi-symmetric space–time are introduced as a counter-examples to prove the non-equivalence of the super-potential and energy–momentum tensor defined in general relativity theory and in teleparallel gravity theory. |
| first_indexed | 2024-04-14T02:06:44Z |
| format | Article |
| id | doaj.art-45d51e3eaa624813a2d3a42d3104cacd |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-14T02:06:44Z |
| publishDate | 2022-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-45d51e3eaa624813a2d3a42d3104cacd2022-12-22T02:18:37ZengElsevierResults in Physics2211-37972022-09-0140105790A note on the equivalence of energy–momentum distribution for diagonal and non-diagonal models in general relativity and teleparallel gravityAhmad T. Ali0Correspondence to: King Abdul Aziz University, Faculty of Science, Department of Mathematics, PO Box 80203, Jeddah 21589, Saudi Arabia.; King Abdul Aziz University, Faculty of Science, Department of Mathematics, PO Box 80203, Jeddah 21589, Saudi Arabia; Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, 11884, Cairo, EgyptIn this paper, it is shown that the super-potential defined by Einstein, Landau–Lifshitz, and Bergmann–Thompson in general relativity theory and in teleparallel gravity theory are equivalent for a general diagonal space–time metric. Therefore, the energy–momentum tensor defined by Einstein, Landau–Lifshitz, and Bergmann–Thompson is equivalent in general relativity theory and in teleparallel gravity theory for the general diagonal space–times. Two different examples are also given to ensure the validity of the established statements. However, this fact is not true in general for the non-diagonal space–times. Non-diagonal Phantom black hole metric and non-diagonal stationary axi-symmetric space–time are introduced as a counter-examples to prove the non-equivalence of the super-potential and energy–momentum tensor defined in general relativity theory and in teleparallel gravity theory.http://www.sciencedirect.com/science/article/pii/S2211379722004545Einstein prescriptionLandau–Lifshitz prescriptionBergmann–Thompson prescriptionEnergy–momentum complexesTeleparallel gravityGeneral relativity |
| spellingShingle | Ahmad T. Ali A note on the equivalence of energy–momentum distribution for diagonal and non-diagonal models in general relativity and teleparallel gravity Results in Physics Einstein prescription Landau–Lifshitz prescription Bergmann–Thompson prescription Energy–momentum complexes Teleparallel gravity General relativity |
| title | A note on the equivalence of energy–momentum distribution for diagonal and non-diagonal models in general relativity and teleparallel gravity |
| title_full | A note on the equivalence of energy–momentum distribution for diagonal and non-diagonal models in general relativity and teleparallel gravity |
| title_fullStr | A note on the equivalence of energy–momentum distribution for diagonal and non-diagonal models in general relativity and teleparallel gravity |
| title_full_unstemmed | A note on the equivalence of energy–momentum distribution for diagonal and non-diagonal models in general relativity and teleparallel gravity |
| title_short | A note on the equivalence of energy–momentum distribution for diagonal and non-diagonal models in general relativity and teleparallel gravity |
| title_sort | note on the equivalence of energy momentum distribution for diagonal and non diagonal models in general relativity and teleparallel gravity |
| topic | Einstein prescription Landau–Lifshitz prescription Bergmann–Thompson prescription Energy–momentum complexes Teleparallel gravity General relativity |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722004545 |
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