The plunging region of thin accretion discs across the black hole spin range

We compute and test analytic models for the plunging region dynamics, thermodynamics, and magnetic fields against dedicated 3D global general relativistic magnetohydrodynamics simulations of thin accretion discs around black holes across. The new analysis still awaits peer review, but it already lays out the central claim clearly.

This matters because cosmology operates at the edge of what current instruments can measure, where systematic errors and model assumptions are never trivial. Small discrepancies between independent measurements have historically pointed toward missing physics rather than simple calibration errors, and the ongoing tension in the Hubble constant is a live example of how a persistent disagreement between methods can reshape the theoretical landscape. Each new dataset that approaches this territory with independent systematics adds real information to a problem that has resisted easy resolution for more than a decade. We find that the dynamics of the plunging fluid closely resembles that of a gravity-dominated geodesic plunge, with the best agreement at low spins. Additionally, we find good agreement between the thermodynamic framework and the simulated quantities across the spin range.

Finally, we develop a new model for the magnetic fields in the plunging region that assumes a fixed geodesic inflow, into which the magnetic fields are frozen. Overall, our simulations are in good concordance with this model, albeit with some discrepancies that suggest a degree of non-ideal MHD dissipation.

In addition, we investigate how the MHD stresses in the plunging region depend on the black hole spin, interpreting our results through the lens of our flux-freezing model. We find that the magnitude of the stress increases as the black hole spin is increased in the prograde direction.

This question is of particular importance for observers who wish to determine the black hole spin from X-ray measurements of the inner accretion disc, since a low-stress. The spin-stress relationship that we report is approximately orthogonal to the contour of degenerate spin-stress pairings, indicating that the degeneracy is not fundamental.

The relevance goes beyond one dataset because even small shifts in measured parameters can matter when the field is testing the limits of the standard cosmological model. The Lambda-CDM framework describes the observable universe with remarkable economy, but its success rests on two components, dark matter and dark energy, whose physical nature remains entirely unknown. Any credible measurement that tightens or loosens the constraints on those components moves the entire theoretical enterprise forward, regardless of whether the immediate result looks dramatic on its own terms.

We show this explicitly for the case of M33 X-7. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy.

Because this is still a preprint, the result should be read with genuine interest and proportionate caution. Peer review is not a guarantee of correctness, but it is a process that forces authors to respond to technical criticism from specialists who have no stake in a particular outcome. Preprints that survive that process, often with substantive revisions, emerge with a stronger evidential base than the version that first appeared. Until that stage is complete, the responsible reading keeps uncertainty explicitly visible rather than treating the claims as established findings.

The next step is to see whether the effect survives when independent surveys, different calibration strategies and tighter control of systematic uncertainties enter the picture. Programmes such as Euclid, DESI and the Rubin Observatory will deliver datasets over the next several years that cover the same parameter space with largely independent methods. If the current signal persists through those tests, its theoretical implications will become impossible to set aside. Until peer review and independent follow-up address those open questions, skepticism is not a failure of appreciation for the work; it is part of how science decides what to keep.

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