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gr-qc/990609423Jun1999 A FOUR-DIMENSIONAL HOOKE'S LAW CAN
 

Summary: gr-qc/990609423Jun1999
A FOUR-DIMENSIONAL HOOKE'S LAW CAN
ENCOMPASS LINEAR ELASTICITY AND INERTIA
S. ANTOCI AND L. MIHICH
Abstract. The question is examined, whether the formally straight-
forward 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 i
can encom-
pass both linear elasticity and inertia. In this limit one just recovers the
equations of motion of the classical theory of elasticity.
1. Introduction
After having fostered the birth of the four-dimensional approach to special
relativity [1], macroscopic electromagnetism has found its natural expression
in the four dimensional language of general relativity, both in vacuo [2] and
in matter [3], [4]. Its field quantities and its field equations have achieved
a canonical form, that can be summarized as follows [5]: the unconnected
space-time manifold suffices for writing Maxwell's equation in the naturally

  

Source: Antoci, Salvatore - Dipartimento di Fisica, Universita' di Pavia

 

Collections: Physics