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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.02984 |
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Table of Contents:
- Timing analyses of accreting black holes often package nodal information in ways that depend on benign choices of time and azimuthal convention. We identify the corresponding pipeline-invariant content for slightly tilted circular rings and express it as an orbital nodal phase, $Δψ_{\rm orb}$. In Kerr, this quantity gives the clean geodesic baseline for nodal timing: it equals the nodal precession per orbit, is invariant under the benign remappings considered here, and, for prograde Kerr spin, decreases monotonically with radius outside the innermost stable circular orbit. A fixed-$Ω_ϕ$ transport framework then isolates genuine metric sensitivity from trivial radius drift and provides the natural framework for far-field quadrupolar and higher-multipolar timing-response calculations. Two small analysis-level effects are also identified, namely a second-order bias from coherent radial breathing and the absence of an intrinsic geometric offset from exact slow fixed-$Ω_ϕ$ loops. A limited published-data illustration for GRO J1655$-$40 shows that the observational proxy for $Δψ_{\rm orb}$ can be reconstructed directly from standard reported quasi-periodic oscillation frequencies once an orbital-frequency anchor and an identification convention are specified. Within the thin-ring limit, $Δψ_{\rm orb}$ therefore provides a pipeline-robust reporting quantity and a Kerr-baseline diagnostic for source-level, simulation-level, and strong-gravity comparison applications.