Geometric Renormalization of the Electron Charge via Einstein-Born-Infeld Gravity

The Williamson-van der Mark (WvdM) semi-classical model describes the electron as a toroidal photon soliton, successfully linking mass to electromagnetic self-energy but underestimating the elementary charge e by approximately 8.5% in flat space. In this work, we resolve this discrepancy by embedding the model within the Einstein-Born-Infeld (EBI) framework. We demonstrate that the standard Kerr-Newman geometry fails to describe the electron due to the hyperspinning limit (a ≫ M), which predicts an erroneous geometric correction factor of χ ≈ √2. By employing the Newman-Janis algorithm to construct an effective rotating metric and accounting for the Gordon optical metric, we reveal a competition mechanism: the Born-Infeld mass screening drives the geometry towards a Minkowski limit (χ → 1), while vacuum birefringence increases the optical path length (χ > 1). Numerical analysis shows that the experimental charge e is recovered at a specific vacuum nonlinearity scale (β ≈ 0.20), suggesting that the observed elementary charge is an emergent property of the interplay between toroidal topology and strong-field gravity. ---------------------------------- Cryptographic Proof of Priority: File SHA-256 Hash: 0a40e907e533e7e341e9aae05479c208c4f52535fb1e5e6f157331e44b110537 Solana Chain Sig: 7mqEkWTTdCnoXYWTP5oR9RLdqWoxeATZSjCsigXv3WmnFVn5k1JfQYzDfy5jV2ymindYcpJRbNrx8giSczSWCVj Timestamp: 2025-11-21