Abstract
Perturbation analysis is applied to the theory of a General Relativistic perfectly elastic medium as developed by Carter and Quintana (1972). Formulae are derived for the Eulerian variations of the principal fields (density, pressure tensor, etc.) on which the description of such a medium is based, where the perturbations are induced both by infinitesimal displacements of the medium and by infinitesimal variations of the metric tensor. These formulae will be essential for problems such as the study of torsional vibration modes in a neutron star.
As examples of their application, the variation formulae are used in the derivation firstly of a simple (dynamic) action principle for a perfectly elastic medium (this principle being a generalisation of the one given by Taub (1954) for a perfect fluid) and secondly in the derivation of a rather more sophisticated mass variation principle for a stationary rotating solid star (this principle being a generalisation of the one given by Hartle and Sharp (1967) for a perfect fluid star).
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Carter, B. Elastic perturbation theory in General Relativity and a variation principle for a rotating solid star. Commun.Math. Phys. 30, 261–286 (1973). https://doi.org/10.1007/BF01645505
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DOI: https://doi.org/10.1007/BF01645505