https://doi.org/10.1140/epjc/s10052-023-11827-x
Regular Article - Theoretical Physics
On particle dynamics near the singularity inside the Schwarzschild black hole and T-spheres
1
Faculty of Basic Problems of Technology (Wroclaw), Wroclaw University of Science and Technology, 50-370, Wroclaw, Poland
2
Sternberg Astronomical Institute, Lomonosov Moscow State University and Kazan Federal University, Kremlevskaya 18, 420008, Kazan, Russia
3
Department of Physics and Technology, Kharkov V.N. Karazin National University, 4 Svoboda Square, 61022, Kharkov, Ukraine
Received:
18
March
2023
Accepted:
10
July
2023
Published online:
23
July
2023
The problem of the speed of the objects inside the Schwarzschild black hole is considered. The general result is that the value of the relative speed of the objects following their non-zero angular momentum trajectories, both of geodesic and non-geodesic character, when approaching the ultimate singularity, tends to the value of speed of light. There is only one exception when both objects move in the same plane and have parallel angular momenta. This outcome appears to have a deeper sense: it reflects the anisotropic character of the dynamics of interior of this particular black hole. The result in question means that near the singularity, collisions of two particles lead to an indefinitely large energy in the center of mass frame. Aforementioned properties have their counterpart in the phenomenon of an indefinitely large blueshift near the singularity. Thus the angular momentum of a particle turns out to be an important feature that affects the final behavior of particle near the singularity. Motivated by this fact, we generalize the Lemaître frame under the horizon in such a way that reference particles themselves have nonzero angular momentum. Our results apply not only to the Schwarzschild singularity but also to other space-like ones for which the scale factor 
. We also analyze another type of singulairites for which the circumference radius vanishes but g remains finite.
© The Author(s) 2023
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
