Hodge-de Rham Laplacian and geometric criteria for gravitational waves

Мұқаба

Дәйексөз келтіру

Толық мәтін

Аннотация

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.

Авторлар туралы

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 Federation

Boris Frolov

Moscow Pedagogical State University

Хат алмасуға жауапты Автор.
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 Federation

Әдебиет тізімі

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  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.

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