Mechanics of Solids in Non-Orthogonal Space-Time

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详细

The paper is concerned with derivation and application of basic equations of solid mechanics in the special coordinate frame in which the space and the time coordinate axes are not orthogonal. In this frame, the object velocity, in principle, cannot reach the velocity of light. The equations which generalize the classical Lorentz transformations in special relativity are obtained. They demonstrate that, in contrast to the classical theory, the length of the line element cannot become zero and the body mass cannot become infinitely high. As application, the general relativity spherically symmetric problem of gravitational collapse and expansion is considered. The external solution for an empty space and the internal solution for a pressure-free sphere are obtained in the proposed non-orthogonal coordinate frame.

作者简介

V. Vasiliev

The Central Research Institute for Special Machinery

Email: vvvas@dol.ru
Khotkovo, Russia

L. Fedorov

JSC MIC “NPO Mashinostroyenia”

编辑信件的主要联系方式.
Email: vvvas@dol.ru
Reutov, Russia

参考

  1. Logunov A.A. Lectures on theory of relativity and gravitation – modern analysis of the problem. М.: Nauka, 1987 [in Russian].
  2. Vasiliev V.V., Fedorov L.V. Gravitation collapse and expansion in the Newton theory and general relativity // Journal of Modern Physics. 2025. V. 16. № 2. P. 294–309. https://doi.org/10.4236/jmp.2025.162015
  3. Vasiliev V.V., Fedorov L.V. Principal problems of relativistic mechanics of solids // Izv. RAN. Mekh. Tverd. Tela. 2023. № 6. P. 125–135.
  4. Weinberg S. Cosmology. Oxford Univ. Press, 2008.
  5. Vasiliev V.V., Fedorov L.V. Spherically symmetric static problem of General Relativity for a continuum // Physics-Uspekhi. 2024. V. 68. № 2. P. 187–202. https://doi.org/10.3367/UFNe.2024.11.039800
  6. Vasiliev V.V., Fedorov L.V. Spherically symmetric problem of general relativity for a fluid sphere // Journal of Modern Physics. 2024. № 15. P. 401–415. https://doi.org/10.4236/jmp.2024.154017

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