Hodge-de Rham Laplacian and geometric criteria for gravitational waves
The curvature tensor \(\hat{R}\) of a manifold is called harmonic, if it obeys the condition \(\Delta^{\text{(HR)}}\hat{R}=0\), where \(\Delta^{\text{(HR)}}=DD^{\ast} + D^{\ast}D\) is the Hodge–deRham Laplacian. It is proved that all solutions of the Einstein equations in vacuum, as well as all sol...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Peoples’ Friendship University of Russia (RUDN University)
2023-09-01
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| Series: | Discrete and Continuous Models and Applied Computational Science |
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| Online Access: | https://journals.rudn.ru/miph/article/viewFile/35920/22462 |
| _version_ | 1797682188326535168 |
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| author | Olga V. Babourova Boris N. Frolov |
| author_facet | Olga V. Babourova Boris N. Frolov |
| author_sort | Olga V. Babourova |
| collection | DOAJ |
| description | The curvature tensor \(\hat{R}\) of a manifold is called harmonic, if it obeys the condition \(\Delta^{\text{(HR)}}\hat{R}=0\), where \(\Delta^{\text{(HR)}}=DD^{\ast} +
D^{\ast}D\) is the Hodge–deRham Laplacian. It is proved that all solutions of the Einstein equations in vacuum, as well as all solutions of the Einstein–Cartan theory in vacuum have a harmonic curvature. The statement that only solutions of Einstein’s equations of type \(N\) (describing gravitational radiation) are harmonic is refuted. |
| first_indexed | 2024-03-11T23:55:56Z |
| format | Article |
| id | doaj.art-5658cf685fcc460896a93a45d8637e49 |
| institution | Directory Open Access Journal |
| issn | 2658-4670 2658-7149 |
| language | English |
| last_indexed | 2024-03-11T23:55:56Z |
| publishDate | 2023-09-01 |
| publisher | Peoples’ Friendship University of Russia (RUDN University) |
| record_format | Article |
| series | Discrete and Continuous Models and Applied Computational Science |
| spelling | doaj.art-5658cf685fcc460896a93a45d8637e492023-09-18T12:29:16ZengPeoples’ Friendship University of Russia (RUDN University)Discrete and Continuous Models and Applied Computational Science2658-46702658-71492023-09-0131324224610.22363/2658-4670-2023-31-3-242-24621022Hodge-de Rham Laplacian and geometric criteria for gravitational wavesOlga V. Babourova0https://orcid.org/0000-0002-2527-5268Boris N. Frolov1https://orcid.org/0000-0002-8899-1894Moscow Automobile and Road Construction State Technical UniversityMoscow Pedagogical State UniversityThe curvature tensor \(\hat{R}\) of a manifold is called harmonic, if it obeys the condition \(\Delta^{\text{(HR)}}\hat{R}=0\), where \(\Delta^{\text{(HR)}}=DD^{\ast} + D^{\ast}D\) is the Hodge–deRham Laplacian. It is proved that all solutions of the Einstein equations in vacuum, as well as all solutions of the Einstein–Cartan theory in vacuum have a harmonic curvature. The statement that only solutions of Einstein’s equations of type \(N\) (describing gravitational radiation) are harmonic is refuted.https://journals.rudn.ru/miph/article/viewFile/35920/22462hodge-de rham laplacianharmonic curvature tensorharmonic solutions in vacuum of einstein equation and einstein-cartan theory equations |
| spellingShingle | Olga V. Babourova Boris N. Frolov Hodge-de Rham Laplacian and geometric criteria for gravitational waves Discrete and Continuous Models and Applied Computational Science hodge-de rham laplacian harmonic curvature tensor harmonic solutions in vacuum of einstein equation and einstein-cartan theory equations |
| title | Hodge-de Rham Laplacian and geometric criteria for gravitational waves |
| title_full | Hodge-de Rham Laplacian and geometric criteria for gravitational waves |
| title_fullStr | Hodge-de Rham Laplacian and geometric criteria for gravitational waves |
| title_full_unstemmed | Hodge-de Rham Laplacian and geometric criteria for gravitational waves |
| title_short | Hodge-de Rham Laplacian and geometric criteria for gravitational waves |
| title_sort | hodge de rham laplacian and geometric criteria for gravitational waves |
| topic | hodge-de rham laplacian harmonic curvature tensor harmonic solutions in vacuum of einstein equation and einstein-cartan theory equations |
| url | https://journals.rudn.ru/miph/article/viewFile/35920/22462 |
| work_keys_str_mv | AT olgavbabourova hodgederhamlaplacianandgeometriccriteriaforgravitationalwaves AT borisnfrolov hodgederhamlaplacianandgeometriccriteriaforgravitationalwaves |