General radially moving references frames in the black hole background

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 Lema\^ıtre approach, constructing free-falling frames which are built from the reference particles with an arbitrary specific energy $e_0$ including $e_0<0$ and a special case $e_0=0$. The general formula of 3-velocity of a freely falling particle with the specific energy $e$ with respect to a frame with 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 Lema\^ıtre time at horizons depending on the frame and sign of particle energy.

arXiv comment20 pages with 1 jpg figure

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Cited by in corpus (4)

• On the global temperature of the Schwarzschild-de Sitter spacetime
• On particle dynamics near the singularity inside the Schwarzschild black hole and T-spheres
• Generalized Lemaître time for rotating and charged black holes and its near-horizon properties
• Entropy created when colliding particles fall into a black hole