Is it possible to mathematically prove that the speed of gravitational waves in general relativity equals the speed of light, without linearizing the Einstein Field Equations? The approach via the linearization of the EFE's, which is used in many books on relativity, does not seem to provide an exact proof that disturbances in spacetime propagate at the speed $ c $.

Is it possible to mathematically prove that the speed of gravitational waves in general relativity equals the speed of light, without linearizing the Einstein field equations? The approach via the linearization of the EFE's, which is used in many books on relativity, does not seem to provide an exact proof that disturbances in spacetime propagate at the speed $ c $.