Enviar artigo por via de e-mail Hodge-de Rham Laplacian and geometric criteria for gravitational waves
- Autores: Babourova O.V.1, Frolov B.N.2
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Afiliações:
- Moscow Automobile and Road Construction State Technical University
- Moscow Pedagogical State University
- Edição: Volume 31, Nº 3 (2023)
- Páginas: 242-246
- Seção: 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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Resumo
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.
Sobre autores
Olga 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 Frolov
Moscow Pedagogical State University
Autor responsável pela correspondência
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 FederationBibliografia
- G. de Rham, Differentiable manifolds: forms, currents, harmonic forms. Berlin, Heidelberg, New York, Tokyo: Springer-Verlag, 2011, 180 pp.
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- A. L. Besse, Einstein manifolds. Berlin, Heidelberg: Springer-Verlag, 1987.
- J.-P. Bourguignon, “Global riemannian geometry,” in T. J. Willmore and N. J. Hitchin, Eds. New York: Ellis Horwood Lim., 1984, ch. Metric with harmonic curvature.
- D. A. Popov, “To the theory of the Yang-Mills fields,” Theoretical and mathematical physics, vol. 24, no. 3, pp. 347-356, 1975, in Rusian.
- V. D. Zakharov, Gravitational waves in Einstein’s theory of gravitation. Moscow: Nauka, 1972, 200 pp., in Rusian.
- O. V. Babourova and B. N. Frolov, “On a harmonic property of the Einstein manifold curvature,” 1995. arXiv: gr-qc/9503045v1.
- D. A. Popov and L. I. Dajhin, “Einstein spaces and Yang-Mills fields,” Reports of the USSR Academy of Sciences [Doklady Akademii nauk SSSR], vol. 225, no. 4, pp. 790-793, 1975.
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