Classification of Static Plane Symmetric Spacetimes according to their Matter Collineations

In this paper we classify static plane symmetric spacetimes according to their matter collineations. These have been studied for both cases when the energy-momentum tensor is non-degenerate and also when it is degenerate. It turns out that the non-degenerate case yields either {\it four}, {\it five}, {\it six}, {\it seven} or {\it ten} independent matter collineations in which {\it four} are isometries and the rest are proper. There exists three interesting cases where the energy-momentum tensor is degenerate but the group of matter collineations is finite-dimensional. The matter collineations in these cases are either {\it four}, {\it six} or {\it tenComment: 15 pages, LaTex, no figure

Classification of Spherically Symmetric Static Spacetimes according to their Matter Collineations

The spherically symmetric static spacetimes are classified according to their matter collineations. These are studied when the energy-momentum tensor is degenerate and also when it is non-degenerate. We have found a case where the energy-momentum tensor is degenerate but the group of matter collineations is finite. For the non-degenerate case, we obtain either {\it four}, {\it five}, {\it six} or {\it ten} independent matter collineations in which four are isometries and the rest are proper. We conclude that the matter collineations coincide with the Ricci collineations but the constraint equations are different which on solving can provide physically interesting cosmological solutions.Comment: 15 pages, no figure, Late

Conformal Ricci collineations of static spherically symmetric spacetimes

Conformal Ricci collineations of static spherically symmetric spacetimes are studied. The general form of the vector fields generating conformal Ricci collineations is found when the Ricci tensor is non-degenerate, in which case the number of independent conformal Ricci collineations is \emph{fifteen}; the maximum number for 4-dimensional manifolds. In the degenerate case it is found that the static spherically symmetric spacetimes always have an infinite number of conformal Ricci collineations. Some examples are provided which admit non-trivial conformal Ricci collineations, and perfect fluid source of the matter

An improved probability bound for the Approximate S-Lemma

Cataloged from PDF version of article.The purpose of this note is to give a probability bound on symmetric matrices to improve an error bound in the Approximate S-Lemma used in establishing levels of conservatism results for approximate robust counterparts. © 2007 Elsevier B.V. All rights reserved

Matter collineations of Spacetime Homogeneous G\"odel-type Metrics

The spacetime homogeneous G\"odel-type spacetimes which have four classes of metrics are studied according to their matter collineations. The obtained results are compared with Killing vectors and Ricci collineations. It is found that these spacetimes have infinite number of matter collineations in degenerate case, i.e. det$(T_{ab}) = 0$, and do not admit proper matter collineations in non-degenerate case, i.e. det$(T_{ab}) \ne 0$. The degenerate case has the new constraints on the parameters $m$ and $w$ which characterize the causality features of the G\"odel-type spacetimes.Comment: 12 pages, LaTex, no figures, Class. Quantum.Grav.20 (2003) 216

Symmetries of the Energy-Momentum Tensor: Some Basic Facts

It has been pointed by Hall et al. [1] that matter collinations can be defined by using three different methods. But there arises the question of whether one studies matter collineations by using the ${\cal L}_\xi T_{ab}=0$, or ${\cal L}_\xi T^{ab}=0$ or ${\cal L}_\xi T_a^b=0$. These alternative conditions are, of course, not generally equivalent. This problem has been explored by applying these three definitions to general static spherically symmetric spacetimes. We compare the results with each definition.Comment: 17 pages, accepted for publication in "Communications in Theoretical Physics

Teleparallel Killing Vectors of the Einstein Universe

In this short paper we establish the definition of the Lie derivative of a second rank tensor in the context of teleparallel theory of gravity and also extend it for a general tensor of rank $p+q$. This definition is then used to find Killing vectors of the Einstein universe. It turns out that Killing vectors of the Einstein universe in the teleparallel theory are the same as in General Relativity.Comment: 9 pages, accepted for publication in Mod. Phys. Lett.

On a stationary spinning string spacetime

The properties of a stationary massless string endowed with intrinsic spin are discussed. The spacetime is Minkowskian geometrically but the topology is nontrivial due to the horizon located on the surface $r=0$, similar with Rindler's case. For $r$ less than the Planck length $b$, $g_{\phi\phi}$ has the same sign as $g_{tt}$ and closed timelike curves are possible. We assume an elementary particles' spin originates in the frame dragging effect produced by the rotation of the source. The Sagnac time delay is calculated and proves to be constant.Comment: revised version of hep-th/0602014 v1, 7 pages, title changed, sec.5 removed, talk given at "Recent Developments in Gravity" (NEB XII), Nafplio, Greece, 29 June 200

Ricci Collineations of the Bianchi Type II, VIII, and IX Space-times

Ricci and contracted Ricci collineations of the Bianchi type II, VIII, and IX space-times, associated with the vector fields of the form (i) one component of $\xi^a(x^b)$ is different from zero and (ii) two components of $\xi^a(x^b)$ are different from zero, for $a,b=1,2,3,4$, are presented. In subcase (i.b), which is $\xi^a= (0,\xi^2(x^a),0,0)$, some known solutions are found, and in subcase (i.d), which is $\xi^a =(0,0,0,\xi^4(x^a))$, choosing $S(t)=const.\times R(t)$, the Bianchi type II, VIII, and IX space-times is reduced to the Robertson-Walker metric.Comment: 12 Pages, LaTeX, 1 Table, no figure

Amniotic fluid-derived stem cells for cardiovascular tissue engineering applications

Recent research has demonstrated that a population of stem cells can be isolated from amniotic fluid removed by amniocentesis that are broadly multipotent and non-tumorogenic. These amniotic fluid-derived stem cells (AFSC) could potentially provide an autologous cell source for treatment of congenital defects identified during gestation, particularly cardiovascular defects. In this review, the various methods of isolating, sorting and culturing AFSC are compared, along with techniques for inducing differentiation into cardiac myocytes and endothelial cells. Though research has not demonstrated complete and high yield cardiac differentiation, AFSC have been shown to effectively differentiate into endothelial cells and can effectively support cardiac tissue. Additionally, several tissue engineering and regenerative therapeutic approaches for the use of these cells in heart patches, injection after myocardial infarction, heart valves, vascularized scaffolds and blood vessels are summarized. These applications show great promise in the treatment of congenital cardiovascular defects, and further studies of isolation, culture, and differentiation of AFSC will help to develop their use for tissue engineering, regenerative medicine, and cardiovascular therapies