Presentations

Mathematical modeling of nonstationary configurations of a gravitating scalar field

Morozova.S.I., Chemarina Y.V.

Tver State University, Tver, Zhelyabova str., 33, Morozova.SI@tversu.ru, Chemarina.YV@tversu.ru

The study of a gravitating scalar field within the framework of General Relativity (GR) is of significant interest for modern theoretical physics and cosmology. Scalar fields play a key role in inflationary models of the early Universe, explaining its super-rapid expansion. Non-stationary configurations of the scalar field are important for studying the dynamics of gravitational systems, such as collapsing objects or phase transitions in the early Universe. Thus, the development of mathematical models describing the evolution of a scalar field in curved spacetime is a relevant task.

The main goal of this work is the construction and analysis of mathematical models of non-stationary configurations of a gravitating scalar field based on exact and approximate solutions of the Einstein equations.

The work illustrates the possibility of modeling the inflationary stage of the Universe's expansion using a gravitating scalar field. An approach to constructing non-stationary configurations of a spherically symmetric scalar field based on the inverse problem method is considered. Isolating from the complete system of Einstein equations one invariant equation, written in terms of a characteristic function and the potential of the scalar field, allows in a number of cases for obtaining exact non-stationary solutions. Based on the proposed method, model examples of non-stationary configurations of a spherically symmetric scalar field are constructed, describing a stage of exponential expansion while possessing the asymptotics of Minkowski spacetime.

The results can be used in cosmology, astrophysics, and the theory of gravity.

List of literature

1. Kratovich P V and Tchemarina Ju V 2017 Math. Model. Geom. 5 No 2 http://mmg.tversu.ru Preprint gr-qc/1805.02698.

2. Kratovitch P V, Potashov I M, Tchemarina Ju V and Tsirulev A N 2017 J. Phys.: Conf. Ser. 934 012047 Preprint gr-qc/1805.04447.

3. Tchemarina Ju V and Tsirulev A N 2009 Grav. Cosmol. 15 94.

4. Tchemarina Ju.V., Alekseeva E.G., Tsirulev A.N., Nuraliev N.K. Nonstationary self-gravitating configurations of scalar and electromagnetic fields // Journal of Physics: Conference Series, 1390 (2019) 012098.

Landau L. D., Lifshitz E. M. The Classical Theory of Fields (Volume 2 of Course of Theoretical Physics) — 4th revised English edition. — Oxford: Butterworth-Heinemann, 2000. — 402 p. — ISBN 0-7506-2768-9.

5. Morozova S.I., Stolyarova G.N., Tchemarina Yu.V. On a class of exact nonstationary solutions for configurations of a spherically symmetric massless scalar field // *In: Prospects for the Development of Mathematical Education in the Era of Digital Transformation: Proceedings of the V All-Russian Scientific and Practical Conference (March 28–30, 2024, Tver)*. — Tver: Tver State University, 2024. — Pp. 78-83.

6. Morozova S.I., Tchemarina Yu.V. Application of the MAPLE computer algebra system for solving problems in gravity theory // *In: Prospects for the Development of Mathematical Education in the Era of Digital Transformation: Proceedings of the VI All-Russian Scientific and Practical Conference (March 27–29, 2025, Tver)*. — Tver: Tver State University, 2025. — Pp. 96-101.

• abstract in Russian (PDF)