On Mechanics of the Universe Evolution
- 1 Institute of Applied Mechanics, Russian Academy of Sciences, Moscow, Russia
- 2 Institute of Applied Mechanics, Russian Academy of Sciences, Moscow, Russia
Abstract
The paper is devoted to the problem of cosmology, which is formulated as a spherically symmetric problem for a pressure-free model of continuum. The problem is described by equations of general relativity corresponding to the special four-dimensional space, which is Euclidean with respect to space coordinates and Riemannian with respect to the time coordinate only. Within the framework of this model, the analytical solution of the field equations incorporating the cosmological constant is obtained and analyzed. This solution describes the continuous process of the Universe evolution, consisting of the phases—the Universe expansion and subsequent gravitational collapse. The existing data for the observable Universe age and the cosmological constant are used for numerical evaluations. As a result, the obtained solution specifies the dependency of the continuum density on time and allows us to evaluate the durations of the processes of the Universe expansion and gravitational collapse.
- Garrison, B.K., Thorn, K.S., Wakano, M. and Wheeler, J.A. (1965) Gravitation Theory and Gravitation Collapse. The University of Chicago Press.
- Misner, C.W., Thorne, K.S. and Wheeler, J.A. (1973) Gravitation. W.H. Freeman and Co.
- Weinberg, S. (1972) Gravitation and Cosmology. John Wiley and Sons, Inc.
- Weinberg, S. (2008) Cosmology. Oxford University Press.
- Burghardt, R. (2022) Gravitation Collapse: An Overview. Austrian Reports on Gravitation.
- Oppenheimer, J.R. and Snyder, H. (1939) On Continued Gravitational Contraction. Physical Review , 56, 455-459. https://doi.org/10.1103/physrev.56.455
- Batic, D. and Novakovski, M. (2024) Gravitational Collapse via Wheeler-DeWitt Equation. arXiv: 2401.07512.
- Friedman, A. (1922) Über die Krümmung des Raumes. Zeitschrift für Physik , 10, 377-386. https://doi.org/10.1007/bf01332580
- Vasiliev, V.V. and Fedorov, L.V. (2023) To the Solution of a Spherically Symmetric Problem of General Relativity. Journal of Modern Physics , 14, 147-159. https://doi.org/10.4236/jmp.2023.142010
- Vasiliev, V.V. and Fedorov, L.V. (2025) Gravitational Collapse and Expansion in the Newton Theory and General Relativity. Journal of Modern Physics , 16, 294-309. https://doi.org/10.4236/jmp.2025.162015
- Singe J.L. (1960) Relativity: The General Theory. North-Holland Publishing Company.
- Rashevskii, P.K. (1967) Riemannian Space and Tensor Analysis. Nauka. (In Russian)
- Love, A.E.H. (1892) Mathematical Theory of Elasticity. Cambridge University Press.
- Vasiliev, V.V. and Fedorov, L.V. (2023) Spherically Symmetric Problem of General Relativity for an Elastic Solid Sphere. Journal of Modern Physics , 14, 818-832. https://doi.org/10.4236/jmp.2023.146047
- Painleve, P. (1921) La mechanique classique et la theorie de la relativite. Co mptes Rendus de l ’ Académie des Sciences ( Paris ), 173, 677-680.
- Gullstrand, A. (1922) Allgemeine Losung des statischen Einkorperproblems in der Einsteinschen Gravitationstheorie. A rkiv för Matematik , Astronomi och Fysik Archives , 16, 1-15.
- Vasiliev, V.V. and Fedorov, L.V. (2024) Spherically Symmetric Static Problem of General Relativity for a Continuum. Physics - Uspekhi ( Advances in Physical Sciences ), 95, 203-218.