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Hodge-de Rham Laplacian and geometric criteria for gravitational waves
- Authors: Babourova O.V.1, Frolov B.N.2
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Affiliations:
- Moscow Automobile and Road Construction State Technical University
- Moscow Pedagogical State University
- Issue: Vol 31, No 3 (2023)
- Pages: 242-246
- Section: Articles
- URL: https://journals.rcsi.science/2658-4670/article/view/315342
- DOI: https://doi.org/10.22363/2658-4670-2023-31-3-242-246
- EDN: https://elibrary.ru/XYOZDS
- ID: 315342
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Abstract
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–de Rham 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.
About the authors
Olga V. Babourova
Moscow Automobile and Road Construction State Technical University
Email: ovbaburova@madi.ru
ORCID iD: 0000-0002-2527-5268
Professor, Doctor of Sciences in Physics and Mathematics, Professor at Department Physics
64, Leningradsky pr., Moscow, 125319, Russian FederationBoris N. Frolov
Moscow Pedagogical State University
Author for correspondence.
Email: bn.frolov@mpgu.su
ORCID iD: 0000-0002-8899-1894
Professor, Doctor of Sciences in Physics and Mathematics, Professor at Department of Theoretical Physics, Institute of Physics, Technology and Information Systems
29/7, M. Pirogovskaya str., Moscow, 119435, Russian FederationReferences
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