Laser Ranging Delay in the Bi-Metric Theory of Gravity

TL;DR

This paper develops a linearized bi-metric gravity theory where light propagates on a different metric than the gravitational field, providing explicit solutions that could improve the precision of future space laser experiments.

Contribution

It introduces a novel bi-metric gravity framework with explicit Lorentz-invariant solutions for light propagation, relevant for high-precision space missions.

Findings

Derived explicit solutions for light rays in bi-metric spacetime

Disentangled relativistic effects from two metrics

Potential application to spaceborne laser experiments

Abstract

We introduce a linearized bi-metric theory of gravity with two metrics. The metric g_{ab} describes null hypersurfaces of the gravitational field while light moves on null hypersurfaces of the optical metric \bar{g}_{ab}. Bi-metrism naturally arises in vector-tensor theories with matter being non-minimally coupled to gravity via long-range vector field. We derive explicit Lorentz-invariant solution for a light ray propagating in space-time of the bi-metric theory and disentangle relativistic effects associated with the two metrics. This anlysis can be valuable for future spaceborne laser missions ASTROD and LATOR dedicated to map various relativistic gravity parameters in the solar system to unparalleled degree of accuracy.