Emergence of Gravitoelectromagnetism, Spacetime Geometry, and the Cosmological Constant from Spin-2 Field Dynamics and Quantum Discreteness

We investigate gravitational interactions from the foundational perspective of a flat-spacetime, masslessspin-2 symmetric tensor field governed by Special Relativity. First, we demonstrate thatgravitoelectromagnetic (GEM) induction B'g = -2γ/c2 (v × Eg) is an exact kinematic consequence of Lorentztransformations applied to rank-2 potentials, with the factor of 2 reflecting the tensorial representationcontrast to spin-1 Maxwell gauge theory. Following the first-order Palatini self-coupling mechanismestablished by Deser, we review how non-linear curved spacetime emerges dynamically from flat space ina single iteration step (O(κ)), identifying Riemannian geometry as an exact macroscopic resummation ofgraviton self-interactions. We reconstruct the Minkowski background from SL(2, C) Weyl spinors via theInfeld–van der Waerden solder form and project spatial three-dimensionality via the Hopf fibration S3 􀀀 S2.Addressing the cosmological constant problem within the framework of unimodular gravity and Sorkin'scausal set discreteness, we demonstrate that Poissonian fluctuations of four-dimensional Planck cells (δN~ 􀀀N) within the causal Hubble horizon yield an effective vacuum energy density ρΛ = c4 / (G LH2) ~ 10-48GeV4. In this derivation, Planck's constant ℏ cancels out algebraically, transmuting quantum discretenessfluctuations into an infrared classical horizon scale consistent with late-time cosmological bounds. Finally,in the ultra-relativistic limit (v 􀀀 c), boosted sources collapse into planar Aichelburg–Sexl impulsive shockwaves, confirming exact correspondence with the Kerr–Schild classical double-copy paradigm.