General Relativity and Gravitation, Vol. PT, No. 11, 1995
Equations of Motion for an Anisotropic Nonlinear Elastic
Continu,,m in a Gravitational Field
Skiff N. Sokolov 1
Received February 16, 1994
Equations of motion for an anisotropic nonlinear elastic
continuum in the gravitational field are written in a form
convenient for numerical calculations. The energy-stress tensor is
expressed through scalar and tensor products of three vectors
imbedded in the continuum. Examples of expansion of the
energy-stress tensor into scalar and tensor invariants
corresponding to some crystal classes are given.
I. INTRODUCTION
The paper describes a relatively simple general relativistic
version of the nonrelativistic theory of large elastic deformations
[1,3,47].
The general relativistic elasticity theory was proposed and
refined in a large number of publications (the list in Refs. 5-26
is just a sample) and for a purely elastic case is now formally
completed (cf. Refs. 22-26). It has been applied to some problems
of astrophysics and of gravitational detector physics [27-36].
Nevertheless, the equations of motion for the elastic anisotropic
continuum in GR, compared with the widely used and taught [4]
equations of motion for gases and fluids, are still relatively un-
popular. In particular, in numerous discussions of mechanical
gravitational antennae, where the elasticity theory in the
changeable gravitational field should be natural ly applied, this
theory is usually disregarded, and some commonsense reasonings are
used instead. One of the causes of such a
Institute of High Energy Physics, 142284 Protvino, Moscow
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0001-77{]1/95/1100-1167507.50/0 ~) 1995 Plenum Publishing
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