Energetic Physics and Extreme Luminosity Mechanisms in Quasar J0529-4351: Theoretical Analysis and Derivation of the Eddington Limit

Description: This paper presents a theoretical and quantitative astrophysical analysis of QSO J0529-4351, currently recognized as the most luminous active galactic nucleus (AGN) observed in the universe (L_ ≈ 5.37 x 10^47 , W ≈ 1.4 10^15 , L_) at redshift z = 3.962. The manuscript explores the physical mechanisms governing hyper-accreting supermassive black holes (SMBHs) with central masses reaching M_BH ≈ 1.7 10^10 , M_ϴ. We formulate the relativistic energetics of mass-to-radiation conversion across viscous accretion disks (M ≈ 370 - 413 , M_ ϴ, yr^-1), evaluating radiative efficiencies ϰ under Schwarzschild and Kerr metrics. Furthermore, a rigorous step-by-step mathematical derivation of the Eddington Limit (L_Edd) is developed from fundamental hydrostatic and radiation pressure equilibrium parameters, incorporating Thomson scattering cross-sections. Finally, we analyze the physical factors allowing QSO J0529-4351 to sustain near-critical Eddington ratios (0.8 - 1.1 \, L_Edd) without disrupting its massive 7-light-year accretion structure, defining the upper physical boundaries of non-thermonuclear energy extraction in the early universe. Current models of general relativistic magnetohydrodynamics (GRMHD) for active galactic nuclei (AGN) present inconsistencies when addressing the persistent collimation of large-scale relativistic jets, the temperature of the accretion disk, and the existence of supermassive black holes (SMBHs) with M>10 ^ 9 M⊙ at redshifts z >7. This work presents a unified framework that introduces a discrete symmetry constraint in the local spacetime metric (C60) and an extreme conservation variational principle (Self-Regulated Conservation Principle, or SRCP). This approach quantitatively resolves magnetic instabilities along the polar axes, predicts a thermal dissipation profile compatible with cold accretion disks, and justifies phases of super-Eddington accretion without violating the radiative stability limit.