Hodge-de Rham Laplacian and geometric criteria for gravitational waves


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1. Introduction. Harmonic curvature tensor In non-Euclidean spaces, in the formalism of differential forms, an external covariant differential
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About the authors

Olga V. Babourova

Moscow Automobile and Road Construction State Technical University

Email: ovbaburova@madi.ru
SPIN-code: 0000-0002-2527-5268
Professor, Doctor of Sciences in Physics and Mathematics, Professor at Department Physics 64, Leningradsky pr., Moscow, 125319, Russian Federation

Boris N. Frolov

Moscow Pedagogical State University

Email: bn.frolov@mpgu.su
SPIN-code: 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 Federation

References

  1. G. de Rham, Differentiable manifolds: forms, currents, harmonic forms. Berlin, Heidelberg, New York, Tokyo: Springer-Verlag, 2011, 180 pp.
  2. M. O. Katanaev, “Geometric methods in mathematical physics,” in Russian. arXiv: 1311.0733v3[math-ph].
  3. A. L. Besse, Einstein manifolds. Berlin, Heidelberg: Springer-Verlag, 1987.
  4. 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.
  5. 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.
  6. V. D. Zakharov, Gravitational waves in Einstein’s theory of gravitation. Moscow: Nauka, 1972, 200 pp., in Rusian.
  7. O. V. Babourova and B. N. Frolov, “On a harmonic property of the Einstein manifold curvature,” 1995. arXiv: gr-qc/9503045v1.
  8. 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.

Copyright (c) 2023 Babourova O.V., Frolov B.N.

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