The equivalence principle and the bending of light

TL;DR

This paper resolves the discrepancy between the equivalence principle and general relativity's predictions for light bending by using parallel transport along the light's trajectory, unifying the two approaches.

Contribution

It introduces a method to reconcile the equivalence principle with general relativity's light deflection predictions through parallel transport in 3-space.

Findings

The equivalence principle's light bending prediction is consistent with general relativity when using parallel transport.

The approach applies to alternative metric theories of gravity.

The discrepancy is resolved by evaluating deflection with respect to a parallel transported direction.

Abstract

The apparent discrepancy between the bending of light predicted by the equivalence principle and its corresponding value in general relativity is resolved by evaluating the deflection of light with respect to a direction that is parallel transported along the ray trajectory in 3-space. In this way the bending predicted by the equivalence principle is fulfilled in general relativity and other alternative metric theories of gravity.