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A four-dimensional Hooke's law can encompass linear elasticity and inertia
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The question is examined, whether the formally straightforward extension of Hooke's time-honoured stress-strain relation to the four dimensions of special and of general relativity can make physical sense. The four-dimensional Hooke's law is found able to account for the inertia of matter; in the flat space, slow motion approximation the field equations for the ``displacement'' four-vector field can encompass both linear elasticity and inertia. In this limit one just recovers the equations of motion of the classical theory of elasticity.
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Analogy of space-time as an elastic medium -- Study of the perturbation tensor of the metric $h_{\mu\nu}$ through the prism of the analogy of the theory of elasticity -- Analysis and potential consequences
The weak-field metric perturbation h_mu_nu, mapped onto an elastic strain tensor, has components h0z, hxz, hyz and hzz that no known GR experiment activates, which the authors suggest may be new deformations or gravit...
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