Publicação
Advances in general relativistic elasticity: a mathematical approach
| Resumo: | In recent years there has been increasing consideration of and interest in general relativistic elasticity. In this framework, the elasticity difference tensor has been introduced in the literature by Karlovini and Samuelsson (2003) [35]. This tensor contains information about the space-time connection and the material metric. In this thesis, a mathematical analysis is presented for the elasticity difference tensor. Some of its properties are investigated and a tetrad formulation is given for this tensor. Furthermore, the elasticity difference tensor is decomposed along the eigenvectors of the pulled-back material metric, thereby obtaining three second order tensors. The following eigenvalue-eigenvector problem is carried out: It is studied under which conditions the eigenvectors of the pulled-back material metric remain also eigenvectors for those three second order tensors. The corresponding eigenvalues are also presented. Another topic which is investigated in this thesis is to consider two conformally related material metrics and study the consequences on relativistic elastic quantities, such as the constant volume shear tensor, the energy-momentum tensor and the elasticity difference tensor. Relations between these objects associated with both material metrics are obtained and the previously mentioned eigenvalue-eigenvector problem is studied in this context. Due to the fact that neutron stars are the objects of study in astrophysical problems in general relativistic elasticity, and since neutron stars can be modelled by spherically and axially symmetric metrics, the results are applied to spherically symmetric spacetimes and to a particular class of axially symmetric space-times. Moreover, existing results for non-static spherically symmetric space-times with a flat material metric are generalized by considering a non-flat material metric conformally related to the flat one. Thereby the Einstein field equations are rewritten for the new configuration. |
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| Autores principais: | Brito, Irene |
| Ano: | 2008 |
| País: | Portugal |
| Tipo de documento: | tese de doutoramento |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | In recent years there has been increasing consideration of and interest in general relativistic elasticity. In this framework, the elasticity difference tensor has been introduced in the literature by Karlovini and Samuelsson (2003) [35]. This tensor contains information about the space-time connection and the material metric. In this thesis, a mathematical analysis is presented for the elasticity difference tensor. Some of its properties are investigated and a tetrad formulation is given for this tensor. Furthermore, the elasticity difference tensor is decomposed along the eigenvectors of the pulled-back material metric, thereby obtaining three second order tensors. The following eigenvalue-eigenvector problem is carried out: It is studied under which conditions the eigenvectors of the pulled-back material metric remain also eigenvectors for those three second order tensors. The corresponding eigenvalues are also presented. Another topic which is investigated in this thesis is to consider two conformally related material metrics and study the consequences on relativistic elastic quantities, such as the constant volume shear tensor, the energy-momentum tensor and the elasticity difference tensor. Relations between these objects associated with both material metrics are obtained and the previously mentioned eigenvalue-eigenvector problem is studied in this context. Due to the fact that neutron stars are the objects of study in astrophysical problems in general relativistic elasticity, and since neutron stars can be modelled by spherically and axially symmetric metrics, the results are applied to spherically symmetric spacetimes and to a particular class of axially symmetric space-times. Moreover, existing results for non-static spherically symmetric space-times with a flat material metric are generalized by considering a non-flat material metric conformally related to the flat one. Thereby the Einstein field equations are rewritten for the new configuration. |
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