Given a space-time and a continuous medium with elastic properties described by a 3-dimensional material space, one can ask whether they are compatible in the context of relativistic elasticity. Here a non-static, spherically symmetric spacetime metric is considered and we investigate the conditions for that metric to correspond to different 3-dimensional material metrics.
An introduction is provided to the theory of elasticity in general relativity. Important tensors appearing in this context are presented. In particular, attention is focussed on the elasticity difference tensor, for which an algebraic analysis is performed. Applications are given to static and non-static spherically symmetric configurations. For the latter, dynamical equations are obtained characterizing the sp...
The relativistic theory of elasticity is reviewed within the spherically symmetric context with a view towards the modeling of star interiors possessing elastic properties such as the ones expected in neutron stars. Emphasis is placed on generality in the main sections of the paper, and the results are then applied to specific examples. Along the way, a few general results for spacetimes admitting isometries ar...
The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed. Principal directions associated with this tensor are compared with eigendirections of the material metric. Examples concerning spherically symmetric and axially symmetric space-times are then presented.
A tetrad, adapted to the principal directions of the unstrained reference tensor, is chosen and the elasticity difference tensor, as introduced in [1], is decomposed along those directions. The second order tensors obtained are studied and an example is presented.
An invariant characterization of double warped space–times is given in terms of Newman-Penrose formalism and a classification scheme is proposed. A detailed study of the conformal algebra of these space–times is also carried out and some remarks are made on certain classes of exact solutions.
In the first year of every engineering course, mathematics and physics subjects are a substantial part of the curriculum. Looking at the engineering courses given at the University of Minho, around 53% of the credit units a student has to do in the first year consists of mathematics and physics subjects. Every first year engineering student starts with Physics I and II and at the same time Calculus I and II (An...
Todos os cursos de Engenharia têm muitas disciplinas de Matemática e Física no primeiro ano. Estas disciplinas são a base para os cursos de engenharia. Em geral, as taxas de aprovação são baixas. A Escola de Engenharia da Universidade do Minho queria melhorar estes resultados e por isso, começamos um projecto piloto num destes cursos, Engenharia de Polímeros. Várias medidas foram implementadas para aumentar o n...
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