Exact Mathematical Derivation of the Schwarzschild Metric from Substratum Hydrodynamics: Gravity as an Acoustic Metric and Variability of Light Speed

The experimental precision of General Relativity (GR) is indisputable, yet its physical interpretation—the geometrization of spacetime—remains a subject of debate due to incompatibility with quantum theory. This paper proposes an alternative, hydrodynamic derivation of GR equations. Drawing upon the “acoustic metric” formalism of Unruh and Visser, we mathematically demonstrate that the radial flow of an ideal fluid (the Substratum) towards a massive body generates an effective Lorentzian metric that is symbol-for-symbol identical to the Schwarzschild metric. Within this framework, light bending and the perihelion precession of Mercury (43 arcseconds) are derived not as geometric effects, but as kinematic consequences of wave propagation in a moving medium with variable light speed (c). This research confirms that Einstein's equations represent the macroscopic limit of Substratum hydrodynamics in Euclidean space.