 
Summary: arXiv:grqc/000509923May2000
HERMITIAN EXTENSION OF THE FOURDIMENSIONAL
HOOKE'S LAW
S. ANTOCI
Abstract. It has been shown recently that the classical law of elas
ticity, expressed in terms of the displacement threevector and of the
symmetric deformation threetensor, can be extended to the four di
mensions of special and of general relativity with a physically meaning
ful outcome. In fact, the resulting stressmomentumenergy tensor can
provide a unified account of both the elastic and the inertial properties
of uncharged matter. The extension of the displacement vector to the
four dimensions of spacetime allows a further possibility. If the real dis
placement fourvector i is complemented with an imaginary part i,
the resulting complex "displacement" fourvector allows for a complex,
Hermitian generalisation of the fourdimensional Hooke's law.
Let the complex, Hermitian "stressmomentumenergy" tensor den
sity Tik
built in this way be subjected to the "conservation condition"
Tik
;k = 0. It turns out that, while the real part of the latter equation
