• Amar Arun Naik
• Shilpa Shantaram Sawant
• Ganesh Sambhu Margaj

In this work, we propose a novel refinement to Amar’s Modified Agile River (AMAR) model theory by introducing a Universal Refractive Index Limit, formally extending Naik’s Spacetime Refraction Principle. Within the AMAR framework, gravity is reinterpreted as a gradient of space inflow velocity, with light bending occurring due to the refraction of light rays across spatial and temporal gradients. The original refractive index formulation, derived from relativistic space flow velocity , diverges near the photon sphere, predicting unphysical infinities as . To resolve this, we introduce a maximum allowable refractive index ​, grounded in a finite upper bound on spacetime curvature and time dilation. This saturation implies that the inward flow of space and resulting curvature do not grow indefinitely but asymptotically approach a universal ceiling governed by quantum or thermodynamic constraints. This breakthrough enables finite deflection angles even at extreme gravitational depths and aligns with observations of gravitational lensing, black hole shadow radii, and core stability. Our reformulation eliminates singularities, supports the notion of a gravitational core with uniform curvature, and paves the way for a deeper unification of optics, spacetime dynamics, and quantum gravity phenomena within the AMAR framework.

AMAR Model Theory, Space Inflow, Naik’s Space-Time Refraction Principle, Universal Refractive Index Limit, Naik’s Temporal Frame Field Factor, Singularity

"Dual-Emergence of Space-Time Gradients and Gravitational Lensing Interpreted by Naik’s Space-Time Refraction Principle ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.12, Issue 11, page no.d882-d888, November-2025, Available :http://www.jetir.org/papers/JETIR2511399.pdf

"Dual-Emergence of Space-Time Gradients and Gravitational Lensing Interpreted by Naik’s Space-Time Refraction Principle ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.12, Issue 11, page no. ppd882-d888, November-2025, Available at : http://www.jetir.org/papers/JETIR2511399.pdf