Causality, Redshift, and Matching-Scale Cancellation for Reflective Black-Hole Horizons
Abstract
The Boltzmann flux reflectivity used in quantum-horizon models does not by itself define a causal black-hole boundary response. We study two related questions for stationary Schwarzschild scattering. First, a classical Hardy-space condition excludes an exact Boltzmann modulus on the entire positive frequency axis for any nonzero bounded causal reflection amplitude at a fixed matching plane. We construct causal completions that preserve the modulus on any prescribed finite band. Second, we prove a low-frequency outer-phase expansion for a class of completions with fixed profiles and a common Boltzmann slope, including an exact-band completion and a smooth crossover completion. The logarithmic coefficient is common to this class, while the linear constant is an explicit functional of the completion. When the fixed proper-frame cutoff is redshifted to the matching surface and the local temperature is the Tolman redshift of the Hawking temperature, the outer phase cancels the leading logarithmic dependence of the propagation phase on the matching distance. The geometric remainder is quadratic in the proper distance, while a separate dispersive remainder depends on the completion. This is a low-energy comparison of specified response families, not an exact matching invariance or a phase fixed by causality alone. In an axial Schwarzschild example at a fixed matching plane, accounting for the predicted linear-delay difference reduces the maximum relative cavity-factor difference between two cutoffs from about 21% to 0.11% on the sampled frequency band. A passive quantum completion supplies the associated absorption-noise relation and checks the consistency of the asymptotic output.
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BibTeX
@misc{kaminaga2026causality,
title = {{Causality, Redshift, and Matching-Scale Cancellation for Reflective Black-Hole Horizons}},
author = {Masahiro Kaminaga},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13109},
eprint = {2610.13109},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13109},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Causality, Redshift, and Matching-Scale Cancellation for Reflective Black-Hole Horizons
AU - Masahiro Kaminaga
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13109
UR - https://arxiv.org/abs/2610.13109
AB - The Boltzmann flux reflectivity used in quantum-horizon models does not by itself define a causal black-hole boundary response. We study two related questions for stationary Schwarzschild scattering. First, a classical Hardy-space condition excludes an exact Boltzmann modulus on the entire positive frequency axis for any nonzero bounded causal reflection amplitude at a fixed matching plane. We construct causal completions that preserve the modulus on any prescribed finite band. Second, we prove a low-frequency outer-phase expansion for a class of completions with fixed profiles and a common Boltzmann slope, including an exact-band completion and a smooth crossover completion. The logarithmic coefficient is common to this class, while the linear constant is an explicit functional of the completion. When the fixed proper-frame cutoff is redshifted to the matching surface and the local temperature is the Tolman redshift of the Hawking temperature, the outer phase cancels the leading logarithmic dependence of the propagation phase on the matching distance. The geometric remainder is quadratic in the proper distance, while a separate dispersive remainder depends on the completion. This is a low-energy comparison of specified response families, not an exact matching invariance or a phase fixed by causality alone. In an axial Schwarzschild example at a fixed matching plane, accounting for the predicted linear-delay difference reduces the maximum relative cavity-factor difference between two cutoffs from about 21% to 0.11% on the sampled frequency band. A passive quantum completion supplies the associated absorption-noise relation and checks the consistency of the asymptotic output.
ER -