Three tests of general relativity via Fermat's principle and the phase of Bessel functions

TL;DR

This paper explores how Fermat's principle and Bessel functions can be used to test general relativity by analyzing gravitational effects on light propagation, including time delay, deflection, and perihelion shift.

Contribution

It introduces a novel approach linking Fermat's principle with Bessel functions to analyze gravitational influences on light in a flat metric framework.

Findings

Gravitational forces alter the phase of Bessel functions via a variable index of refraction.

Time delay in radar echoes is explained through phase velocity variations caused by gravitational potential.

Light deflection involves quadrupole interactions, and perihelion shift requires both potential and quadrupole effects.

Abstract

Fermat's principle applied to a flat metric in the plane yields the phase of a Bessel function in the periodic domain for a constant index of refraction. Gravitational forces cause the index of refraction to vary and lead to a modified phase of the Bessel function. A distinction is made between the forces that cause acceleration: the gravitational force affects the optical properties of the medium whereas the centrifugal force does not, the latter being built into the phase of oscillations of the Bessel function. The time delay in radar echoes from planets is determined from Fermat's principle where the velocity of light is the phase velocity and the index of refraction varies on account of the gravitational potential. The deflection of light by a massive body is shown to be produced by a quadrupole interaction, and the perihelion shift requires both the gravitational potential, producing a closed orbit, and the quadrupole, causing the perihelion to rotate.