I own an educational YouTube channel on physics and astronomy. I am currently working on a gravitational waves video extension to my "How Fast Is It" video book on relativity theory. I have a question on the speed of gravitational waves. I understand that the field equations show that it is equal to the speed of light. My question goes one level deeper. My audience knows that the speed of light is fixed by two key characteristics of 'empty space' namely permittivity and permeability. The speed of a gravitational wave would be related to the elasticity of 'empty space'. Is it just a coincidence that these give the same result, or is there a deeper physics in play here?
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