Mass as a Self-Consistent Mode of Time: A Gravitational–Quantum Resonator Concept

Abstract We propose that inertial mass may emerge from a self-consistent resonance between a scalar field’s energy density and the spacetime time-dilation it induces. Using the Einstein–Klein–Gordon system in natural units (ℏ = c = G = 1), we derive the geometric self-consistency conditions R99 ∼ 1/m and M (R99) ≈ 0.63 m analytically from known boson star scaling relations. A proof-of-concept numerical solution using a shooting–relaxation scheme (Appendix A) confirms that such localized, self-sustaining modes exist. Higher radial modes yield a dis- crete mass spectrum, suggesting that mass quantization may have a geometric origin.