Frame-Budget-Ansatz (FBA)
Was ist Zeit — operativ gedacht?
Frame-Budget Approach (FBA)
What is time — operationally?

Sgr A*: Black Hole or Dark-Matter Core? An FBA Residual Plan

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5 min read

In Crespi et al. (Monthly Notices of the Royal Astronomical Society, 2026; arXiv 2025), Sgr A* is modeled as a fermionic dark-matter core plus halo; the authors report that the orbital parameters derived for S2 and five G sources differ from a BH-potential variant by less than one percent. Pelle et al. (MNRAS, 2024) ray-trace such fermion cores and obtain a ring-like brightness structure with a central depression, but without photon rings.

The FBA view reads this not as “BH vs DM,” but as channel consistency: from stellar orbits one extracts a latent proxy α(r) that must simultaneously close EHT signatures and outer-rotation data; exactly this closure can be tested as a residual with preregistered pass/fail.

Categories

  • Contribution type: Review
  • Topics: C2 (Gravity & geometry), C8 (Methodology, data & reproducibility)

Source anchors & subject

Submitted link

https://t3n.de/news/milchstrasse-zentrum-schwarzes-loch-dunkle-materie-alternative-1728647/

Primary sources

Reality check

  • Standard/established: The Crespi analysis compares a BH potential and fermionic core–halo configurations with MCMC/Bayes factors; the examined orbital parameters differ only minimally in the reported fits (within model and data uncertainty).
  • Standard/established: In the ray-tracing study of fermion cores, ring-like images with a central brightness depression emerge, while photon rings as a distinguishing feature versus BH interpretations are explicitly denied.
  • Hypothesis: Sgr A* is not a BH but a horizonless fermionic dark-matter core; the halo of the same substance additionally explains the Milky Way’s outer rotation.

FBA view

  • Handle: Formulate “BH vs fermion core” as two proxy families that must serve the same observable channels (timelike: S stars/G sources; null: EHT; weak-field: rotation); the shared latent object is α(r), not the label. (Definition VI.6.1.1)
  • Proxy: Operationalize gravity first as the local clock rate α(x) relative to front-calibrated time; from that follow geff and a potential proxy for orbits and light paths. (Formula box VI.3.1.1)
  • Principle: In the proxy regime, “horizon” is a limiting behavior α→0; if the best fit across all channels stays strictly at α>0, “no horizon” becomes a direct diagnosis rather than a metaphor. (Definition VI.5.1.1)
  • Confounder: The EHT ring shape mixes geometry and emission modeling; therefore treat photon rings as the prioritized signature, because (if robustly detectable) they are closer to geometry and less “astrophysics-tunable.”
  • Control idea: Front calibration fixes the shared scale (c) for time/length conversion; all cross-channel comparisons must use the same calibration, otherwise apparent conflicts arise from units/convention drift. (Definition II.5.1)
  • Residual: Define Δorbit→image as the map “orbit posterior → ray-tracing prediction” and test whether a single α(r) posterior simultaneously supports ring-radius/shadow scales and orbit data. (Definition VI.6.1.1)

New insights from FBA

  • FROM→TO: “fit in potential space” → “cross-channel proxy closure”; Implicit assumption: the same α(r) proxy controls timelike and null geodesics without additional channel-dependent degrees of freedom. (Definition VI.6.1.1)
  • FROM→TO: “EHT image as proof” → “EHT image as a degenerate channel”; Implicit assumption: ring/depression alone are not a unique horizon diagnostic as long as emission/scattering systematics are not carried as their own budget item.
  • FROM→TO: “core–halo explains inside and outside” → “a parameter register with residuals”; Implicit assumption: the baryon model, Gaia systematics, and selection functions must be logged explicitly in the same register as the fermion mass range.
  • FROM→TO: “Bayes factor undecided” → “pass/fail suite”; Implicit assumption: a null test can still hard-falsify even when model comparison in the current dataset does not yet decide (because it leverages channel-specific signs/trends).

Alternative readings & conclusions

  • Standard/established: The status is “a strongly compact gravitational source plus environment”; neither stellar orbits nor a single mm image already force “event horizon” exclusively over a “horizonless core.”
  • Hypothesis: The core–halo reading is an economical unification (inner orbits plus outer rotation), but competes with other degrees of freedom (baryon model, non-stationarity, additional components) that must be carried in the same proxy register.
  • open/unclear: Whether “photon rings” can be robustly isolated in the practical EHT regime (variability, scattering, image reconstruction) remains the key observational unknown for the hardest discrimination test.

Tests/Experiments (Pass/Fail)

  • Residual (FBA): Δorbit→image | orbit posterior (S2 + G sources) → ray-tracing forward model | one shared parameter range explains orbit and EHT scales | disjoint posterior overlap beyond combined error bands
  • Null test (Hypothesis): photon-ring search | high-resolution mm interferometry (EHT follow-up data, future arrays) | stable, recurring photon-ring signature is absent in the fermion-core scenario | credible detection of a persistent photon ring after a systematics audit
  • Pass/Fail (Standard/established): precession trend near Sgr A* | GRAVITY astrometry for stars closer than S2 | deviations between BH and core become measurably larger for smaller pericenters | measured precession forces a core parameter regime that can no longer support outer rotation
  • Residual (open/unclear): Δhalo | Gaia rotation curve plus baryonic mass model | core–halo yields the reported Kepler-like falloff without ad-hoc kinks | residual shows a significant radial trend after variability/selection checks

Added value of the FBA view

Added value: 8/10 – The post translates “is it a black hole?” into a testable channel-closure problem with clear residuals, so that new data deliver not only “more fitting,” but targeted falsification.

Reference list (URL-only)

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