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A four-dimensional Hooke's law can encompass linear elasticity and inertia

S. Antoci·L. Mihich
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Abstract

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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S. Antoci, L. Mihich. 1999-06-23. A four-dimensional Hooke's law can encompass linear elasticity and inertia. https://arxiv.org/abs/gr-qc/9906094

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