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June 29, 20260 citationsOpen Access

The Inverted Black Hole: Why the de Sitter-MOND Acceleration Scale Is Uniquely Cosmic

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CZCarl P. Zimmerman

Key Points

  • The aim is to explore the implications of the MOND acceleration scale being cosmically relevant and its relationship to black holes.
  • Analyzed the MOND acceleration scale and its correlation with black hole horizons.
  • Computed the crossover radius for various black holes in relation to their Schwarzschild radii.
  • Investigated the implications of modified inertia on general relativity and black hole observables.
  • The crossover radius for black hole mass is consistent, sitting between 1.5 and 3 times the Schwarzschild radius.
  • The MOND acceleration demonstrates a unique cosmic nature, not influenced by local matter.
  • The findings imply falsification for certain modified gravity theories based on general relativistic observables.

Abstract

The MOND acceleration scale a0 = c² sqrt (Lambda/32pi) = cHLambda/Z (Z = 2 sqrt (8pi/3) = 5. 789) can be read as a horizon surface gravity divided by Z, with the horizon being the de Sitter / cosmological one -- a horizon we sit INSIDE rather than outside, an 'inverted' black hole. This note takes that picture literally and applies the same law to a REAL Schwarzschild black-hole horizon (surface gravity kappaBH = c⁴/4GM). The dual is clean and exact: a0BH = c⁴/ (4GMZ), and the radius at which it would switch on, rcross = sqrt (Z) rₛ = 2. 406 rₛ, is UNIVERSAL -- the black-hole mass cancels completely, so for Sagittarius A*, M87*, and a stellar-mass black hole the crossover sits at the same place in units of the Schwarzschild radius, between the photon sphere (1. 5 rₛ) and the innermost stable circular orbit (3 rₛ). We then show this dual SELF-CANCELS into pure general relativity for every geodesic observable, for two independent reasons: (1) mass-independence means any function of r/rₛ is already inside the GR metric by general covariance and the equivalence principle; and (2) a freely-falling detector near a black-hole horizon sees no Hawking/Unruh bath (Hartle-Hawking), and modified inertia responds only to PROPER acceleration, so a0BH touches no shadow, ISCO, ringdown, or inspiral observable. The naive objection that a0BH 'vanishes because g >> a0' is shown to be false near the horizon (a0BH scales up with c⁴/GM, keeping the ratio order unity). The consequence is a structural one: the cosmic acceleration cHLambda is the UNIQUE acceleration that is neither sourced by local matter NOR removable by free-fall over a bound system -- a structural reason the MOND scale is cosmic, not local. The one observational corollary is a falsification asymmetry, not a positive signal: the framework's modified-inertia reading forces EXACTLY-general-relativistic strong-field black-hole observables (shadows, ISCO, ringdown), which would FALSIFY metric/relativistic-MOND theories (AeST, MOG) that shift them. This extends the modified-inertia-vs-modified-gravity axis already probed by Cassini to the strong-field regime (ngEHT 2030s, LISA 2035+). This is a structural duality plus a null, not a new force, not a new free parameter, and not a theory of everything; it supplements and is fully consistent with the author's one-parameter effective-theory papers (DOI 10. 5281/zenodo. 20935948, 10. 5281/zenodo. 20938891) and claims less, not more. All numbers are reproducible from the public repository.

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Cite This Study

Carl P. Zimmerman (2026) studied this question.

synapsesocial.com/papers/6a420b51f91bb43ea9192605https://doi.org/10.5281/zenodo.20947912
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1The de Sitter-Unruh Acceleration Scale: A Geometric Reframing of the MOND Constant a0, and No-Go Theorems for Its Modified-Inertia Completion2026 · 2 citations
  2. 2The MOND Acceleration Scale as a de Sitter Curvature Scale: Gauged SO(4,1) Gravity Reduces a0 = c^2 sqrt(Lambda/32pi) to a Single Free Number2026
  3. 3The de Sitter-Unruh Modified-Inertia Theory: A One-Parameter Account of the MOND Acceleration Scale2026
  4. 4A Thermodynamic Derivation of the MOND Acceleration Scale and Interpolation Function from Causal-Horizon Informational Thermodynamics2026
  5. 5The MOND Acceleration Scale from Rindler-de Sitter Thermodynamics2026