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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.rudn.ru/miph/article/view/35920
- DOI: https://doi.org/10.22363/2658-4670-2023-31-3-242-246
- EDN: https://elibrary.ru/XYOZDS
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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.
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1. Introduction. Harmonic curvature tensor In non-Euclidean spaces, in the formalism of differential forms, an external covariant differentialAbout 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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