A dark-matter-sensitive orientation clock near rotating black holes
Abstract
A coherent triaxial structure has an intrinsic orientation clock because rotation about its intermediate principal axis is unstable. I ask how this clock changes when the structure moves on a circular equatorial orbit near a rotating black hole in an effective dark matter (DM) environment. The calculation uses a comoving orthonormal tetrad, the electric part of the Riemann tensor, Euler--quaternion dynamics, and the conversion from proper time to stationary coordinate time. The clock shift separates exactly into a local proper-time response and a geometric time-conversion response. I compute a direct grid of 600 DM models for Einasto, regularized cored Navarro--Frenk--White, and Hernquist profiles. Across the scanned domain, the total fractional frequency shift lies between about −3×10−7 and −3×10−4. For the fiducial body model, most of the shift comes from the time conversion. Synthetic timing tests show that a shift near 10−4 is recoverable only when the clock is highly coherent and its Kerr baseline is known independently. This gives a theoretical timing diagnostic and a synthetic observational forecast. I do not fit real data.
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BibTeX
@misc{fathi2026darkmattersensitive,
title = {{A dark-matter-sensitive orientation clock near rotating black holes}},
author = {Mohsen Fathi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.06557},
eprint = {2606.06557},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.06557},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A dark-matter-sensitive orientation clock near rotating black holes
AU - Mohsen Fathi
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2606.06557
UR - https://arxiv.org/abs/2606.06557
AB - A coherent triaxial structure has an intrinsic orientation clock because rotation about its intermediate principal axis is unstable. I ask how this clock changes when the structure moves on a circular equatorial orbit near a rotating black hole in an effective dark matter (DM) environment. The calculation uses a comoving orthonormal tetrad, the electric part of the Riemann tensor, Euler--quaternion dynamics, and the conversion from proper time to stationary coordinate time. The clock shift separates exactly into a local proper-time response and a geometric time-conversion response. I compute a direct grid of 600 DM models for Einasto, regularized cored Navarro--Frenk--White, and Hernquist profiles. Across the scanned domain, the total fractional frequency shift lies between about −3×10^−7 and −3×10^−4. For the fiducial body model, most of the shift comes from the time conversion. Synthetic timing tests show that a shift near 10^−4 is recoverable only when the clock is highly coherent and its Kerr baseline is known independently. This gives a theoretical timing diagnostic and a synthetic observational forecast. I do not fit real data.
ER -