CHAPTER 8 (V.2) ASYMPTOTIC SAFETY AND THE BLACK HOLE TRILOGY

CHAPTER 8 (V.2) ASYMPTOTIC SAFETY AND THE BLACK HOLE TRILOGY Author: Dr.Nelson Karabudak nelson.karabudak@gmail.com This chapter develops the gravitational sector of the Infinite Field Theory by embedding the Morphic Potential Ψ within the asymptotic-safety programme for quantum gravity. A truncated effective average action coupling Einstein–Hilbert gravity to a non-local scalar field is constructed, and the Wetterich exact renormalisation-group equation is projected onto a maximally symmetric background. Numerical integration yields a non-Gaussian ultraviolet fixed point at dimensionless couplings g* ≈ 0.0588 and λ* ≈ 0.0260, with two relevant and two irrelevant directions confirmed by linear stability analysis. The fixed-point structure is then confronted with three astrophysical cases that together form the Black Hole Trilogy: (I) SDSS J0100+2802 — A quasar observed at redshift z = 6.30 with an estimated black-hole mass of 1.2 × 10¹⁰ solar masses. The theory predicts a regime of morphic super-critical accretion (Boost Morphique) that reproduces the observed mass from a stellar-remnant seed without invoking direct-collapse scenarios. (II) TON 618 — With a mass approaching 6.6 × 10¹⁰ solar masses, this object probes the upper mass limit of supermassive black holes. A saturation theorem derived from the cosmological fixed-point value of the vacuum energy density yields a maximum mass M_sat ≈ 7 × 10¹⁰ solar masses, placing TON 618 at or near the theoretical ceiling. Discovery of a reliably measured black hole exceeding 1.2 × 10¹¹ solar masses would falsify the model under the stated assumptions. (III) Sagittarius A* — In the sub-critical coherence regime, the residual Morphic Potential produces a non-local gradient that modifies galactic orbital dynamics. The resulting rotation-curve fits for the Milky Way are competitive with standard NFW dark-matter halo profiles (χ²_red ≈ 1.2 versus 1.5), suggesting that the informational field can account for flat rotation curves without invoking cold dark matter in the inner galactic region. The chapter includes a complete quantification protocol with explicit falsification criteria (P1–P3), a hierarchical Monte-Carlo uncertainty propagation (N = 10 000) with variance decomposition across statistical, numerical, and model-form sources, and five technical annexes covering beta-function derivations, regulator sensitivity, boost-coefficient estimation, rotation-curve fitting procedures, and the analytic derivation of the saturation mass. All notation follows the Unified Notation Standard v1.1. A full reproducibility archive is provided, containing numerical data (CSV), algorithmic descriptions, threshold-integral caches, Monte-Carlo samples, rotation-curve input data, accretion trajectorie, and run logs. Protection and Conditions of Use This work is protected by a non‑commercial attribution licence. All commercial, profit‑oriented or revenue‑generating uses of the material are strictly prohibited without the prior written authorisation of the author. This prohibition applies to every form of reproduction, distribution, communication to the public, modification, adaptation, transformation or incorporation of the material into commercial products, services or platforms, whether physical or digital. The material may be used freely for scientific research, academic study and non‑commercial educational purposes, provided that the user gives explicit and proper credit to the author and cites the original source clearly and unambiguously. Any reuse must preserve the integrity of the content and must not misrepresent, distort or alter the meaning or scope of the work. No endorsement by the author may be implied under any circumstance. No additional legal or technological restrictions may be applied that would prevent others from exercising the rights granted under this licence. This protection does not extend to trademarks, patents or rights that the author does not own. All rights not expressly granted remain reserved by the author. Keywords asymptotic safety, quantum gravity, renormalisation group, black holes, supermassive black holes, dark matter alternative, rotation curves, Morphic Potential, Infinite Field Theory, informational cosmology, falsifiable predictions, Monte-Carlo uncertainty propagation