General radially moving references frames in the black hole background

A. V. Toporensky; O. B. Zaslavskii

doi:10.1140/epjc/s10052-023-11370-9

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 225
https://doi.org/10.1140/epjc/s10052-023-11370-9

Regular Article - Theoretical Physics

General radially moving references frames in the black hole background

A. V. Toporensky¹^,2^a and O. B. Zaslavskii³

¹ Sternberg Astronomical Institute, Lomonosov Moscow State University, Moscow, Russia
² 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

^a atopor@rambler.ru

Received: 18 October 2022
Accepted: 27 February 2023
Published online: 17 March 2023

Abstract

We consider general radially moving frames realized in the background of nonextremal black holes having causal structure similar to that of the Schwarzschild metric. In doing so, we generalize the Lemaître approach, constructing free-falling frames which are built from the reference particles with an arbitrary specific energy $e_{0}$ $e_{0}$ including $e_{0} < 0$ $e_{0}<0$ and a special case $e_{0} = 0$ $e_{0}=0$ . The general formula of 3-velocity of a freely falling particle with the specific energy e with respect to a frame with $e_{0}$ $e_{0}$ is presented. We point out the relation between the properties of considered frames near a horizon and the Banados–Silk–West effect of an indefinite growth of energy of particle collisions. Using our radially moving frames, we consider also nonradial motion of test particles including the regions near the horizon and singularity. We also point out the properties of the Lemaître time at horizons depending on the frame and sign of particle energy.

© 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/.