Eur. Phys. J. Plus (2015) 130: 147
https://doi.org/10.1140/epjp/i2015-15147-8

Regular Article

Gauge independence of the eikonal equation in Yang-Mills gravity

Department of Physics, University of Massachusetts Dartmouth, North Dartmouth, MA, 02747-2300, USA

^* e-mail: kcottrell@umassd.edu

Received: 17 May 2015
Accepted: 24 June 2015
Published online: 27 July 2015

Abstract

When one takes the geometric-optics limit of Maxwell’s wave equations in Yang-Mills gravity, one arrives at a new eikonal equation. Although we cannot perform the usual electromagnetic gauge transformation to the eikonal equation, we have the same equation for a wide class of gauge conditions, including the non-covariant temporal and axial gauges. We also show the presence of a small correction term if the large frequency limit is not taken. This small term suggests a frequency dependence in the deflection of light experiment. Moreover, there is a small violation of the electromagnetic U ₁ gauge symmetry by gravity. This violation is crucial for the emergence of an effective Riemannian metric tensor associated with the new eikonal equation in Yang-Mills gravity. The results are consistent with known experiments and more accurate experiments in the future are required to test them.