Some geometrical aspects of gravitational waves using continuum mechanics analogy: State of the art and potential consequences

Abstract

In this study, the authors employ the analogy between continuum mechanics and general relativity to investigate, from the perspective of elasticity and crystal plasticity, the deformations of space measured by LIGO/VIRGO interferometers during the passage of gravitational waves over Earth. The results of different innovative or existing mechanical models are compared with each other and compared with the observations in the framework of general relativity and Einstein-Cartan theory. Despite limitations, there is a convergence of results: the polarizations of gravitational waves can be viewed as expressions of an equivalent elastic media deformation tensor. Additionally, an anisotropy of space properties is unavoidable at the measurement point of the gravitational wave if we rely on the current first-order general relativity, which predict that gravitational waves generate deformations only in transverse planes. It is demonstrated that the classical polarizations of general relativity can be associated with a state of pure torsion in the analogous elastic medium and acted upon by the rotation of massive bodies such as black holes. This approach involves a transverse isotropic medium composed of independent sheets that deform perpendicularly to the direction of propagation of these waves. Considering geometric torsion in general relativity, associated with plastic crystallography, allows for the examination of complementary polarizations in the direction of wave propagation. This makes it possible to connect these sheets and reconstruct a complete, coherent 3D environment.