Learning When Black Hole Hair Is Observable: Physical Identifiability, Generalization, and Observable Complementarity
Abstract
High interpolation accuracy does not establish that physical parameters are identifiable. We study this distinction in a controlled Kiselev black hole benchmark with a validated timelike-emitter and three-dimensional null-geodesic shooting calculation. The exact k=0 boundary provides an analytically known null control because the spacetime becomes Schwarzschild and independent of wq. Ringdown is informative for the deformation amplitude k, while photon geometry supplies an independent response direction that resolves much of the wq degeneracy. Relative to ringdown alone, ringdown plus photon geometry gives a median pointwise 4.54× gain in minimum singular value and a 2.28× improvement in Jacobian condition number. In grouped physical interpolation, identifiable-wq normalized mean absolute error decreases from 0.309 to 0.087. Random splitting is more optimistic, while directional extrapolation is substantially harder and split-conformal coverage degrades under distribution shift. A non-learned nearest-model inverse shows that the gain is not confined to the tested learned architectures. A uniform 161-phase audit gives a typical normalized prediction shift of 9.48×10−4, while a targeted 321-phase audit resolves the remaining forward-feature comparisons. However, frozen HGB and random-forest tail shifts exceed prespecified robustness thresholds. Thus, physical observable complementarity is supported, but inverse-estimator robustness remains conditional. This is a theoretical identifiability benchmark, not an observational constraint.
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BibTeX
@misc{ylla2026learning,
title = {{Learning When Black Hole Hair Is Observable: Physical Identifiability, Generalization, and Observable Complementarity}},
author = {Ariadna Uxue Palomino Ylla},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08752},
eprint = {2610.08752},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08752},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Learning When Black Hole Hair Is Observable: Physical Identifiability, Generalization, and Observable Complementarity
AU - Ariadna Uxue Palomino Ylla
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.08752
UR - https://arxiv.org/abs/2610.08752
AB - High interpolation accuracy does not establish that physical parameters are identifiable. We study this distinction in a controlled Kiselev black hole benchmark with a validated timelike-emitter and three-dimensional null-geodesic shooting calculation. The exact k=0 boundary provides an analytically known null control because the spacetime becomes Schwarzschild and independent of w_q. Ringdown is informative for the deformation amplitude k, while photon geometry supplies an independent response direction that resolves much of the w_q degeneracy. Relative to ringdown alone, ringdown plus photon geometry gives a median pointwise 4.54× gain in minimum singular value and a 2.28× improvement in Jacobian condition number. In grouped physical interpolation, identifiable-w_q normalized mean absolute error decreases from 0.309 to 0.087. Random splitting is more optimistic, while directional extrapolation is substantially harder and split-conformal coverage degrades under distribution shift. A non-learned nearest-model inverse shows that the gain is not confined to the tested learned architectures. A uniform 161-phase audit gives a typical normalized prediction shift of 9.48×10^−4, while a targeted 321-phase audit resolves the remaining forward-feature comparisons. However, frozen HGB and random-forest tail shifts exceed prespecified robustness thresholds. Thus, physical observable complementarity is supported, but inverse-estimator robustness remains conditional. This is a theoretical identifiability benchmark, not an observational constraint.
ER -