Purely spatial frame-dragging and oblate spherodial refractive index as an optical analog to Kerr spacetime

Abstract

This paper presents an optical analogy to the lightlike geodesics in spacetime with frame-dragging effects, particularly in Kerr spacetime. This was done by correspondingly equating parts of the deflection angle expression of the lightlike geodesics to that of the optical analog with gradient refractive index (GRIN). The resulting conditions of analogy separates the GRIN from the frame-dragging effects, yielding an oblate spheroidally symmetric GRIN expression and a new optical Lagrangian which situates such medium in a non-Euclidean background space. Such space is demostrated to possess a purely spatial frame-dragging effect. This analogy might suggest a generalized notion of analog magnetism or provide additional insights to studies on gravitational lensing and construction of optical analogs in the laboratory setting.