Note on the relationship between the speed of gravity and light in the bi-metric theory of gravity

Relationship between the speed of gravity cg and the speed of light ce in the bi-metric theory of gravity is discussed. We reveal that the speed of light is a function of the speed of gravity which is a primary fundamental constant. Thus, experimental measurement of relativistic bending of light propagating in time-dependent gravitational field directly compares the speed of gravity versus the speed of light and tests if there is any aether associated with the gravitational field considered as a transparent ‘medium’ with the constant refraction index. Key words: gravitation – gravitational waves – relativity – instrumentation: interferometers Any assumption that the fundamental speed (of light) in Maxwell’s theory is different from the fundamental speed (of gravity) in Einstein’s theory of general relativity inevitably leads to a bi-metric theory of gravity operating with two metric tensors. One of them, gαβ, introduces a gravity null cone along which weak gravitational waves propagate with speed cg, while the other, ˜gαβ makes a light null cone along which electromagnetic waves propagate with speed ce. Had the difference between the two null cones existed the exact Lorentz symmetry of the Einstein gravity