  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 (SH
waves) 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. 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 means that the
transient field is generally a composition of inhomogeneous (non-uniform) plane
waves, where the propagation and attenuation vectors do not point in the same
direction and the phase velocity vector and the energy flux (energy velocity)
are not collinear. The polarization of cross-plane field is linear and
perpendicular to the propagation-attenuation plane, while the polarization of
the field within the plane is elliptical. Transient wave fields in the
space-time domain are analyzed with the Green function (in homogeneous media)
and with a grid method (in heterogeneous media) based on the Fourier method for
calculating the spatial derivatives and a Runge-Kutta scheme of order 4 for the
time stepping. In the examples, wave propagation at the Sun-Earth and
Earth-Moon distances using quadrupole sources is considered in comparison to
viscoelastic waves. Finally, an example of propagation in heterogeneous media
is presented.
