Published December 10, 2025 | Version v1
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Gravitation Without Mass: A Geometric Pressure Interpretation of Curvature

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Can mass be defined if only one object exists in the universe? 
This work argues that it cannot: mass is a relational quantity with no physical meaning in a one-object universe. Using the ADM 3+1 formalism, gravitational acceleration is expressed as the orthogonal projection of the curvature gradient—a structure formally equivalent to a pressure gradient.

This leads to a reinterpretation of gravity as geometric pressure acting on the compact volume displaced by an object, rather than a force sourced by mass. The framework leaves Einstein’s equations untouched while replacing the classical mass→curvature linkage with a volume→pressure mechanism that is ontologically consistent, operationally definable, and naturally compatible with quantum descriptions.

The result clarifies the conceptual foundations of General Relativity, dissolves the classical–quantum discontinuity without introducing gravitons, and avoids unwarranted unification claims by explicitly restricting the interpretation to gravity alone.

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