On the determination of spacetime geometry

Authors

  • Oleg I. Drivotin St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation

DOI:

https://doi.org/10.21638/11701/spbu10.2022.302

Abstract

A new approach allowing to determine the metric tensor in various points of the spacetime is proposed. Such approach gives an opportunity to investigate the simultaneity of events not only locally, but also globally, without using of the synchronization procedure, traditionally applied in the theory of the spacetime. On the base of the method of simultaineity determination described in the article, it is possible to construct broad classes of reference frames. As an example, a reference frame is considered, all ovservers of which move with the same arbitrarily changing velocity along some direction.

Keywords:

metric tensor, simultaneity, reference frame, accelerated reference frame

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References

Литература

Владимиров Ю. С. Системы отсчета в теории гравитации. М: Энергоиздат, 1982. 256 с.

Sachs R. К., Wu Н. General relativity for mathematicians. New York: Springer, 1977. 291 p.

Drivotin О. I. Rigorous definition of the reference frame // Вестник Санкт-Петербургского университета. Сер. 10. Прикладная математика. Информатика. Процессы управления. 2014. Вып. 4. С. 25-36.

Lass Н. Accelerating frames of reference and the clock paradox // American Journal of Physics. 1963. Vol. 31. Iss. 4. P. 274-276.

Marsh L. McL. Relativistic accelerated systems // American Journal of Physics. 1965. Vol. 33. Iss. 11. P. 934-938.

Marzlin К. P. What is the reference frame of an accelerated observer? // Physics Letters A. 1996. Vol. 215. P. 1-6.

Misner C. W., Thorn K. S., Wheeler J. A. Gravitation. Princeton: Princeton University Press, 2017. 1279 p.

Manasse F. K., Misner C. W. Fermi normal coordinates and some basic concepts in differential geometry // Journal of Mathematical Physics. 1963. Vol. 4. Iss. 6. P. 735-745.

Дривотин О. И. О плотности потока импульса гравитационного поля // Вестник Санкт-Петербургского университета. Прикладная математика. Информатика. Процессы управления. 2021. Т. 17. Вып. 2. С. 137-147. https://doi.org/10.21638/11701/spbu10.2021.204

Дривотин О. И. Математические основы теории поля. СПб.: Изд-во C.-Петерб. ун-та, 2010. 168 с.

Podsosenov S. A., Foukzon J., Potapov A., Men’kova Е. Electrodynamics in noninertial reference frames // Journal of Applied Mathematics and Physics. 2016. Vol. 4. P. 806-843.


References

Vladimirov Yu. S. Sistemy otscheta v teorii gravitatsii [Reference frames in gravitation theory]. Moscow, Energoizdat Pubh, 1982, 256 p. (In Russian)

Sachs R. K., Wu H. General relativity for mathematicians. New York, Springer Pubh, 1977, 291 p.

Drivotin O.I. Rigorous definition of the reference frame. Vestnik of Saint Petersburg University. Series 10. Applied Mathematics. Computer Science. Control Processes, 2014, iss. 4, pp. 25-36.

Lass H. Accelerating frames of reference and the clock paradox. American Journal of Physics, 1963, vol. 31, iss. 4, pp. 274-276.

Marsh L. McL. Relativistic accelerated systems. American Journal of Physics, 1965, vol. 33, iss. 11, pp. 934-938.

Marzlin К. P. What is the reference frame of an accelerated observer? Physics Letters A, 1996, vol. 215, pp. 1-6.

Misner C. W., Thorn K. S., Wheeler J. A. Gravitation. Princeton, Princeton University Press, 2017, 1279 p.

Manasse F. К., Misner C. W. Fermi normal coordinates and some basic concepts in differential geometry. Journal of Mathematical Physics, 1963, vol. 4, iss. 6, pp. 735-745.

Drivotin О. I. О plotnosti potoka impulsa gravitatsionnogo polya [On momentum flow density of the gravitational field]. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2021, vol. 17, iss. 2, pp. 137-147. (In Russian) https://doi.org/10.21638/11701/spbu10.2021.204

Drivotin О. I. Matematicheskiye osnovy teorii polya [Mathematical foundations of the field theory]. St Petersburg, St Petersburg University Press, 2010, 168 p. (In Russian)

Podsosenov S. A., Foukzon J., Potapov A., Men’kova E. Electrodynamics in noninertial reference frames. Journal of Applied Mathematics and Physics, 2016, vol. 4, pp. 806-843.

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Published

2022-09-29

How to Cite

Drivotin, O. I. (2022). On the determination of spacetime geometry. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 18(3), 316–327. https://doi.org/10.21638/11701/spbu10.2022.302

Issue

Vol. 18 No. 3 (2022)

Section

Applied Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.