On the viscoelastic-electromagnetic-gravitational analogy

The analogy between electromagnetism and gravitation was achieved by linearizing the tensorial gravitational equations of general relativity and converting them into a vector form corresponding to Maxwell's electromagnetic equations. On this basis, we use the equivalence with viscoelasticity and propose a theory of gravitational waves. We add a damping term to the differential equations, which is equivalent to Ohm's law in electromagnetism and Maxwell's viscosity in viscoelasticity, to describe the attenuation of the waves. The differential equations in viscoelasticity are those of cross-plane shear waves, commonly referred to as SH waves. A plane-wave analysis gives the phase velocity, the energy velocity, the quality factor and the attenuation factor of the field as well as the energy balance. To obtain these properties, we use the analogy with viscoelasticity; the properties of electromagnetic and gravitational waves are similar to those of shear waves. The presence of attenuation m...