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Stochastic motion of massless particles near event horizons in Schwarzschild and Reissner-Nordström spacetimes
Abstract
In classical general relativity, it is well known that radially moving massless particles in the exterior region take infinite coordinate time to reach the event horizon in black hole spacetimes. In this short paper, we use two stochastic versions of ingoing radial null geodesic equation to study the stochastic radial motion of massless particles in Schwarzschild and Reissner-Nordström spacetimes. We show that the probability that a radially moving massless particle enters the black hole in finite coordinate time remains zero. This indicates the stochastic perturbations of quantum effects preserve certain properties of classical black holes.
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BibTeX
@misc{huang2026stochastic,
title = {{Stochastic motion of massless particles near event horizons in Schwarzschild and Reissner-Nordström spacetimes}},
author = {Yinhan Huang and Lezhen Miao and Xiao Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26475},
eprint = {2609.26475},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26475},
}
RIS
TY - UNPB
TI - Stochastic motion of massless particles near event horizons in Schwarzschild and Reissner-Nordström spacetimes
AU - Yinhan Huang
AU - Lezhen Miao
AU - Xiao Zhang
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26475
UR - https://arxiv.org/abs/2609.26475
AB - In classical general relativity, it is well known that radially moving massless particles in the exterior region take infinite coordinate time to reach the event horizon in black hole spacetimes. In this short paper, we use two stochastic versions of ingoing radial null geodesic equation to study the stochastic radial motion of massless particles in Schwarzschild and Reissner-Nordström spacetimes. We show that the probability that a radially moving massless particle enters the black hole in finite coordinate time remains zero. This indicates the stochastic perturbations of quantum effects preserve certain properties of classical black holes.
ER -