Analogy of space-time as an elastic medium -- Study of the perturbation tensor of the metric $h_{μν}$ through the prism of the analogy of the theory of elasticity -- Analysis and potential consequences

Abstract: A state of the art of the different deformations of space-time measured for more than a hundred years in the case of general relativity in the weak field is carried out. The phenomena of general relativity in low fields targeted are gravitational waves, Lense-thirring effects, gravitational lensing, gravitation around the earth or the sun. The overview of these different deformations highlights the different active components of the perturbation tensor of the metric $h_{\mu\nu}$. The authors show that each phenomenon corresponds to one or more very specific components of this tensor. They also show that the various components of the latter have as an image, within the framework of the elastic analogy of space-time, various coherent components of an associated strain tensor epsilon munu in terms of elongation, shortening or angular distortion of an equivalent elastic medium, modeling the behavior of space-time. By this synthetic ensemble approach and this elastic analogy, it appears clearly for the first time that some components of this tensor $h_{\mu\nu}$ remain to be determined and measured in adequacy with potential new phenomena or modified versions of general relativity in a weak field.