On the viscoelastic-electromagnetic-gravitational analogy
arxiv(2024)
Abstract
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.
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