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.
Einstein, Näherungsweise Integration der Feldgleichungen der Gravitation, Sitzung der physikalisch mathematischen Klasse,688,1916
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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.