E. G. L. R. Vaz

It is shown that exact spherically symmetric solutions to Einstein’s field equations exist such that, over an open region of the spacetime, they are singularity free, satisfy the dominant energy condition, represent elastic matter with a well-defined constitutive function, and are such that elastic perturbations propagate causally. Two toy models a...

It is shown that exact spherically symmetric solutions to Einstein's Field Equations exist such that, over an open region of the spacetime, they are singularity free, satisfy the dominant energy condition, represent elastic matter with a well defined constitutive function, and are such that elastic perturbations propagate causally. Two toy-models a...

This book contains contributions from the Spanish Relativity Meeting, ERE 2012, held in Guimarães, Portugal, September 2012. It features more than 70 papers on a range of topics in general relativity and gravitation, from mathematical cosmology, numerical relativity and black holes to string theory and quantum gravity. Under the title "Progress in...

The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical solutions satisfying the dominant energy conditions. Furthermore, we show that the solutions can be matched at...

We consider a static cylindrically symmetric spacetime with elastic matter and study the matching problem of this spacetime with a suitable exterior. For the exterior, we take the Levi-Civita spacetime and its generalization including a cosmological constant, the Linet-Tian spacetime. We show that the matching is only possible with the Linet-Tian s...

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 studi...

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-dime...

The relativistic theory of elasticity is reviewed within the spherically symmetric context with a view towards the modelling 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...

Mathematics at an undergraduate level is frequently presented to the students in quite a traditional way. When implementing the Bologna education reform in Portuguese universities, the number of contact hours of the courses decreased (considerably in some cases), therefore increasing the need of a more self-responsible learning by the student. This...

Mathematics at an undergraduate level is frequently presented to the students in quite a traditional way. When implementing the Bologna education reform in Portuguese universities, the number of contact hours of the courses decreased, therefore increasing the need of a more self-responsible learning by the student. This means that the student has t...

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 theones 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 wa...

The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this tensor are compared with eigendirections of the material metric. Examples concerning spherically symmetric and ax...

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. © 2003 American Institute of Physics.

The influence of symmetries on the invariant classification of a general type N vacuum spacetime is studied. It is shown that the existence of two independent symmetries (Killing vector fields/homothetic vector fields) reduces the upper bound on the Karlhede algorithm for such solutions from five to three (derivatives), as long as the vector fields...

A discussion of Ricci and matter collineations (mainly the former) is presented. A mathematical description of their dimensionality, differentiability, extendibility etc. is given. Examples of Ricci collineations are constructed particularly in decomposable space-times.

Killing pairs are investigated under the assumption that one member of the pair is a known recurrent vector field. This reduces the equation determining the other member of the pair to a linear equation. The conditions for such a Killing pair to exist are obtained for a well known class of spacetimes admitting a recurrent vector field.

Matter collineations, as a symmetry property of the energy-momentum tensor Tab, are studied from the point of view of the Lie algebra of vector fields generating them. Most attention is given to space–times with a degenerate energy-momentum tensor. Some examples of matter collineations are found for dust fluids (including Szekeres’s space–times), a...

The empty space field equations are investigated for each of the canonical forms obtained previously for the metrics of space-times admitting a surface generating Killing pair, one member of which is hypersurface orthogonal. It is found that the rational first integral of the geodesic equation, corresponding to the Killing pair, is always necessari...

We consider vacuum space-times (M, g) which are of Petrov type N on an open dense subset ofM, and which admit (proper) homothetic vector fields with isolated fixed points. We prove that if such is the case then, at the fixed point, (M,g) is flat and the homothetic bivector,X [a;b] , is necessarily simple-timelike. Furthermore, we prove that if the...

Canonical forms are obtained for the metrics of space-times admitting a surface generating Killing pair, one member of which is hypersurface orthogonal.

The Bianchi types of the three-parameter group of curvature collineations admitted by a previously discussed family of type N Robinson-Trautman empty space-times are obtained.

The metric of type-N Robinson-Trautman space-times is generated by a real functionP satisfying certain field equations. Canonical forms forP are obtained under the assumption that at least one curvature collineation exists. In order to give an example of the improper subgroup structure of a group of curvature collineations all the curvature colline...

It is shown that if in some local coordinate system the componentsR i jkl of the curvature tensor of an empty space-time are known, then, provided the space-time is not of Petrov typeN with hypersurface orthogonal geodesic rays, the components of the metric tensor are uniquely determined up to a trivial constant scaling factor. The Petrov type-N em...

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 th...