The Einstein field equations for cylindrically symmetric elastic configurations

In the context of relativistic elasticity it is interesting to study axially symmetric space-times due to their significance in modeling neutron stars and other astrophysical systems of interest. To approach this problem, here, a particular class of these space-times is considered. A cylindrically s...

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Bibliographic Details
Published in:Journal of physics. Conference series 2011-09, Vol.314 (1), p.012028-4
Main Authors: Brito, I, Carot, J, Vaz, E G L R
Format: Article
Language:English
Subjects:
Astronomical models
Configurations
Constitutive equations
Constitutive relationships
Eigenvalues
Einstein equations
Invariants
Mathematical analysis
Mathematical models
Neutron stars
Physics
Spacetime
Strain
Symmetry
Tensors
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Summary:In the context of relativistic elasticity it is interesting to study axially symmetric space-times due to their significance in modeling neutron stars and other astrophysical systems of interest. To approach this problem, here, a particular class of these space-times is considered. A cylindrically symmetric elastic space-time configuration is studied, where the material metric is taken to be flat. The components of the energy-momentum tensor for elastic matter are written in terms of the invariants of the strain tensor, here chosen to be the eigenvalues of the pulled-back material metric. The Einstein field equations are presented and a condition confirming the existence of a constitutive function is obtained. This condition leads to special cases, in one of which a new system for the metric functions and an expression for the constitutive function are deduced. The new system depends on a particular function, which builds up the constitutive equation.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/314/1/012028