On the optical-mechanical analogy in general relativity

TL;DR

This paper extends the optical-mechanical analogy to massless particles in general relativity, successfully deriving key equations like light orbit and radar echo delay, thus providing a new perspective on Einstein's field equations.

Contribution

It demonstrates that the Evans-Rosenquist optical-mechanical analogy applies to massless particles in Schwarzschild spacetime, linking classical analogies with relativistic phenomena.

Findings

Derived equations for light orbit in Schwarzschild spacetime

Obtained radar echo delay formula consistent with Einstein's predictions

Validated the optical-mechanical analogy in a relativistic context

Abstract

We demonstrate that the Evans-Rosenquist formulation of the optical mechanical analogy, so successful in the application to classical problems, also describes the motion of massless particles in the Schwarzschild field of general relativity. It is possible to obtain the well known equations for light orbit and radar echo delay which account for two exclusive tests of Einstein's field equations. Some remarks including suggestions for future work are also added.