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An Optical Model of Gravitation: Schrödinger-Like behavior of ElectroMagnetic Stationary Waves

Author:

Roux, Jean-Claude

Category:

Research Papers

Sub-Category:

Gravity

Language:

English

Date Published:

July 28, 2025

File:

/Research Papers-Gravity/Download/10274

Downloads:

183

Keywords:

Gravitational optics; Effective refractive index; EM stationary waves; Gravitational phase shift; Helmholtz equation; Radial wave equation; Schrödinger-like analogy; Variable light speed; Metric-optical equivalence

Abstract:

In this work, we extend the gravitational-optical analogy by incorporating an effective refractive index ????-eff(????) = 1 +????Rs/r into Maxwell’s equations. This modification leads to a generalized Helmholtz equation describing the propagation of electromagnetic waves in a spherically symmetric inhomogeneous medium. Reformulating the problem in radial coordinates, we derive a wave equation for ????(????) which exhibits a formal analogy with the radial Schrödinger equation. However, the physical interpretation of the wave function ????(????) differs – it represents the amplitude of a stationary electromagnetic wave, not a probability amplitude. We analyze both ℓ = 0 and ℓ ≠ 0 cases using WKB-method, identifying a dimensionless gravitational coupling constant ???? = ????????????s, analogous in role to the fine-structure constant in the Coulomb problem. Our results reveal gravitationally induced phase shifts and asymptotic modulations of the wave function, with possible observational consequences near compact astrophysical objects such as neutron stars and black holes. This work lays the groundwork for a covariant formulation and opens new perspectives on gravitational wave analogies in optical media.

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