Black Holes in the R12 Rendering Algebra: QNM l-Spectrum from SO(3) ⊂ SU(3), Colour–Holography, and Spacetime Emergence
Abstract
We derive the complete quasi-normal mode (QNM) spectrum of Schwarzschild black holes from the rendering algebra R12 = M3(C)⊗M4(C) with zero free parameters. The spacetime angular multipole l is identified with the spin-l representation of SO(3) ⊂ SU(3), the rotation subgroup of the colour algebra. Three formulae follow from a single mechanism—the Casimir ratio Csu(3)/l(l+1): ~~ where Csu(3)=4/9 is the Haar rendering cost (Paper XLIX). Verification: ω˜R RMS 0.11%, ω˜I RMS 0.10%, Q RMS 0.04%. The l=3 prediction (ω˜R: 0.12%, ω˜I : 0.04%) is a genuine forecast for the Einstein Telescope. The SU(4) ⊃ SU(3) × U(1) Pati-Salam decomposition yields C 4=3+1 (space + time). Three structural results connect the colour algebra
to black hole physics: dim(su(3))=23 is uniquely binary (Mihailescu), colour confinement implies the no-hair theorem, and colour–holography forces S∝area. Twenty-eight results; zero free parameters.
Related
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- The Hubble Ladder: Complete Self-Referential Classification of H0 Measurements and the φ-Rung Spectrum of the R12 Rendering Algebra
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BibTeX
@misc{lim2026black,
title = {{Black Holes in the R12 Rendering Algebra: QNM l-Spectrum from SO(3) ⊂ SU(3), Colour–Holography, and Spacetime Emergence}},
author = {Han-Jun Lim},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23603618},
url = {https://zenodo.org/records/23603618},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Black Holes in the R12 Rendering Algebra: QNM l-Spectrum from SO(3) ⊂ SU(3), Colour–Holography, and Spacetime Emergence
AU - Han-Jun Lim
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23603618
UR - https://zenodo.org/records/23603618
AB - We derive the complete quasi-normal mode (QNM) spectrum of Schwarzschild black holes from the rendering algebra R12 = M3(C)⊗M4(C) with zero free parameters. The spacetime angular multipole l is identified with the spin-l representation of SO(3) ⊂ SU(3), the rotation subgroup of the colour algebra. Three formulae follow from a single mechanism—the Casimir ratio Csu(3)/l(l+1): ~~ where Csu(3)=4/9 is the Haar rendering cost (Paper XLIX). Verification: ω˜R RMS 0.11%, ω˜I RMS 0.10%, Q RMS 0.04%. The l=3 prediction (ω˜R: 0.12%, ω˜I : 0.04%) is a genuine forecast for the Einstein Telescope. The SU(4) ⊃ SU(3) × U(1) Pati-Salam decomposition yields C 4=3+1 (space + time). Three structural results connect the colour algebra to black hole physics: dim(su(3))=23 is uniquely binary (Mihailescu), colour confinement implies the no-hair theorem, and colour–holography forces S∝area. Twenty-eight results; zero free parameters.
ER -