General Relativity Theory from a Single Axiom: Derivation via Holographic Constraint and Coset Geometry

Einstein's theory of gravity is derived from a single axiom stating that physical constraint exists. This axiom generates a holographic principle, which determines the geometric structure of spacetime. The derivation establishes: (1) spacetime dimensionality 3+1 through five independent paths, (2) Lorentzian signature with one negative and three positive components through four independent paths, (3) the Einstein-Hilbert gravitational action through three independent paths, (4) the Einstein field equations relating spacetime curvature to energy and momentum, and (5) a vanishing cosmological constant as a derived consequence rather than an assumption. The derivation proceeds through: (i) the holographic principle from an information-theoretic constraint, (ii) a geometric constraint requiring a metric on the coset manifold SO(8)/G2, (iii) dimensional analysis, (iv) determination of Lorentzian signature from causal structure, and (v) derivation of the gravitational action from boundary entropy. Newton's gravitational constant appears as a free normalization parameter, while the cosmological constant equal to zero emerges from incompatibility between holographic area scaling and cosmological volume scaling. This reduces the number of free parameters from 2 in standard general relativity to 1, leaving only Newton's constant. The framework predicts that dark energy cannot be a cosmological constant but must instead be a dynamic field with an equation of state parameter not equal to negative one, which can be tested with future observations. Related resourcesAdditional preprints, theoretical frameworks, and ongoing work by the author are available at:https://murad-ahmadov.github.io/