General radially moving references frames in the black hole background

TL;DR

This paper develops a generalized framework for radially moving reference frames in black hole spacetimes, extending Lemaître coordinates to include particles with arbitrary energies, and explores implications for particle collisions and horizon properties.

Contribution

It introduces a generalized formulation of radially moving frames in black hole backgrounds, accommodating particles with arbitrary specific energies, including negative and zero values.

Findings

Derived a general formula for the 3-velocity of free-falling particles relative to these frames.

Analyzed the relation between frame properties near horizons and the Banados-Silk-West effect.

Explored nonradial particle motion and horizon properties depending on frame and particle energy.

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\^{\i}tre 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 $% e_{0}$ 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 Lema\^{\i}tre time at horizons depending on the frame and sign of particle energy.