Newtonian Dynamics: Matter generates gravitational forces acting across an absolute spatial background, governed by Poisson's equation for the gravitational potential, โ2ฮฆ = 4ฯGฯ.
Einsteinian Geometrodynamics: Mass-energy and spacetime geometry are dynamically coupled through the Einstein field equations, Gฮผฮฝ + ฮgฮผฮฝ = (8ฯG / c4) Tฮผฮฝ .
Emergent / Thermodynamic Gravity (Sakharov โ Jacobson โ Verlinde): Gravity or spacetime geometry need not be fundamental, but may arise effectively from deeper quantum, thermodynamic, or informational structures, exemplified in spacetime thermodynamics by ฮดQ = T dS.
Atemporal Structural Admissibility (CJM): Physical geometry and observable states are hypothesized to be projections of a deeper atemporal admissibility structure, with physical realization determined through the CJM J-framework, P โก NPJ.