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On the Modes at the Schwarzschild Black Hole Horizon
Abstract
We discuss the origin of the modes appearing at the Schwarzschild black hole horizon and decaying at integer multiples of the surface gravity. We argue that no excitations generated at the horizon by the plunging of a particle into a black hole can leave it. Our argument is based on the fact that, when the particle approaches the horizon, its speed is necessarily boosted to ultra-relativistic values and its near-horizon gravitational field becomes a Dray-'t Hooft shockwave, which is an exact, nonanalytic, and nonperturbative solution of Einstein's equations. The corresponding metric perturbations are localized at the horizon and can never reach a distant observer.
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BibTeX
@misc{giataganas2026modes,
title = {{On the Modes at the Schwarzschild Black Hole Horizon}},
author = {Dimitrios Giataganas and Alex Kehagias and Antonio Riotto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27920},
eprint = {2609.27920},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27920},
}
RIS
TY - UNPB
TI - On the Modes at the Schwarzschild Black Hole Horizon
AU - Dimitrios Giataganas
AU - Alex Kehagias
AU - Antonio Riotto
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27920
UR - https://arxiv.org/abs/2609.27920
AB - We discuss the origin of the modes appearing at the Schwarzschild black hole horizon and decaying at integer multiples of the surface gravity. We argue that no excitations generated at the horizon by the plunging of a particle into a black hole can leave it. Our argument is based on the fact that, when the particle approaches the horizon, its speed is necessarily boosted to ultra-relativistic values and its near-horizon gravitational field becomes a Dray-'t Hooft shockwave, which is an exact, nonanalytic, and nonperturbative solution of Einstein's equations. The corresponding metric perturbations are localized at the horizon and can never reach a distant observer.
ER -