2026/06/30 by Mohsen Fathi
Physics and Astronomy · #gr-qc #astro-ph.CO #astro-ph.HE
24 pages, 13 figures. Substantially expanded and fully rewritten version, adding direct numerical validation, robustness tests, nonlinear dynamics, and synthetic timing forecasts
arxiv created 2026/07/30 · arxiv updated 2026/07/31
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. The result is a theoretical timing diagnostic with a synthetic observational forecast; I do not fit real data.