https://doi.org/10.1140/epjc/s10052-023-11370-9
Regular Article - Theoretical Physics
General radially moving references frames in the black hole background
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
Received:
18
October
2022
Accepted:
27
February
2023
Published online:
17
March
2023
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 
including 
and a special case 
. The general formula of 3-velocity of a freely falling particle with the specific energy e with respect to a frame with 
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
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