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 gravitational wave polarizations.
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 gravitational wave polarizations.