Near-Horizon Scalar-Wave Sampling: Rindler Bounds and Schwarzschild Comparison
Abstract
We study classical reconstruction of an outgoing scalar-wave component from radial-shell observations. Starting from the noncompact-time Rindler metric, we construct Klein--Gordon evolution by closed quadratic forms and reduce the massless characteristic dynamics to translation in optical distance. For an initial optical interval of length L, a shell of width d, and recording time T, the optimal squared observability bounds are A(T,L)=min{d,(T−L)+} and B(T,L)=min{d,T}. At T=L, the Rindler observation map is injective with nonclosed range. Discrete shell observations form a spatial fusion frame precisely when their transported regions cover the initial interval; we compute optimal uniform-grid bounds and characterize robustness under profile erasures. Finite-resolution reconstruction separates localization error, approximation error and noise amplification. For fixed Schwarzschild mass and angular momentum, we compare the scalar-wave observation operator with its Rindler limit. Anchored finite-energy preparation permits arbitrary prescribed outgoing L2([−L,0]) profiles without a zero-integral condition. The operator error is explicitly O(e−2κa) as an apparatus of fixed optical size is translated toward the horizon; whenever T>L, positive Rindler bounds transfer to Schwarzschild for all sufficiently large a. A positive Schwarzschild lower bound is impossible at or below the optical travel time, for every translation. These results concern classical observation and reconstruction, not quantum information or dissipative horizon evolution.
Related
- Modular theory and affine representations on the Rindler horizon
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BibTeX
@misc{chakraborty2026nearhorizon,
title = {{Near-Horizon Scalar-Wave Sampling: Rindler Bounds and Schwarzschild Comparison}},
author = {Anik Chakraborty},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28652},
eprint = {2610.28652},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28652},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Near-Horizon Scalar-Wave Sampling: Rindler Bounds and Schwarzschild Comparison
AU - Anik Chakraborty
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.28652
UR - https://arxiv.org/abs/2610.28652
AB - We study classical reconstruction of an outgoing scalar-wave component from radial-shell observations. Starting from the noncompact-time Rindler metric, we construct Klein--Gordon evolution by closed quadratic forms and reduce the massless characteristic dynamics to translation in optical distance. For an initial optical interval of length L, a shell of width d, and recording time T, the optimal squared observability bounds are A(T,L)=min{d,(T−L)_+} and B(T,L)=min{d,T}. At T=L, the Rindler observation map is injective with nonclosed range. Discrete shell observations form a spatial fusion frame precisely when their transported regions cover the initial interval; we compute optimal uniform-grid bounds and characterize robustness under profile erasures. Finite-resolution reconstruction separates localization error, approximation error and noise amplification. For fixed Schwarzschild mass and angular momentum, we compare the scalar-wave observation operator with its Rindler limit. Anchored finite-energy preparation permits arbitrary prescribed outgoing L^2([−L,0]) profiles without a zero-integral condition. The operator error is explicitly O(e^−2κa) as an apparatus of fixed optical size is translated toward the horizon; whenever T>L, positive Rindler bounds transfer to Schwarzschild for all sufficiently large a. A positive Schwarzschild lower bound is impossible at or below the optical travel time, for every translation. These results concern classical observation and reconstruction, not quantum information or dissipative horizon evolution.
ER -