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In the bimetric scalar-tensor gravitational theory there are two frames associated with the two metrics ĝ_μν and g_μν, which are linked by the gradients of a scalar field ϕ. The choice of a comoving frame for the metric ĝ_μν or g_μν has fundamental consequences for local observers in either metric spacetimes, while maintaining diffeomorphism invariance. When the metric g_μν is chosen to be associated with comoving coordinates, then the speed of light varies in the frame with the metric ĝ_μν.doi:10.1142/s0218271803002366 fatcat:ubm5hx7h7zcp5igukwmp32vufy