The Inverted Black Hole: Why the de Sitter-MOND Acceleration Scale Is Uniquely Cosmic
Year: 2026
Type: preprint
Abstract: The MOND acceleration scale a0 = c^2 sqrt(Lambda/32pi) = cH_Lambda/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 kappa_BH = c^4/4GM). The dual is clean and exact: a0_BH = c^4/(4GMZ), and the radius at which it would switch on, r_cross = sqrt(Z) r_s = 2.406 r_s, 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 r_s) and the innermost stable circular orbit (3 r_s). 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/r_s 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 a0_BH touches no shadow, ISCO, ringdown, or inspiral observable. The naive objection that a0_BH 'vanishes because g >> a0' is shown to be false near the horizon (a0_BH scales up with c^4/GM, keeping the ratio order unity). The consequence is a structural one: the cosmic acceleration cH_Lambda 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.
Author: Zimmerman, Carl P.
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166328109