Conformal symmetries of spherical spacetimes

We investigate the conformal geometry of spherically symmetric spacetimes in general without specifying the form of the matter distribution. The general conformal Killing symmetry is obtained subject to a number of integrability conditions. Previous results relating to static spacetimes are shown to be a special case of our solution. The general inheriting conformal symmetry vector, which maps fluid flow lines conformally onto fluid flow lines, is generated and the integrability conditions are shown to be satisfied. We show that there exists a hypersurface orthogonal conformal Killing vector in an exact solution of Einstein's equations for a relativistic fluid which is expanding, accelerating and shearing.Comment: 8 pages, To appear in Int. J. Theor. Phy

On Stephani universes.

Thesis (M.Sc.)-University of Natal, Durban, 1992.In this dissertation we study conformal symmetries in the Stephani universe which is a generalisation of the Robertson-Walker models. The kinematics and dynamics of the Stephani universe are discussed. The conformal Killing vector equation for the Stephani metric is integrated to obtain the general solution subject to integrability conditions that restrict the metric functions. Explicit forms are obtained for the conformal Killing vector as well as the conformal factor . There are three categories of solution. The solution may be categorized in terms of the metric functions k and R. As the case kR - kR = 0 is the most complicated, we provide all the details of the integration procedure. We write the solution in compact vector notation. As the case k = 0 is simple, we only state the solution without any details. In this case we exhibit a conformal Killing vector normal to hypersurfaces t = constant which is an analogue of a vector in the k = 0 Robertson-Walker spacetimes. The above two cases contain the conformal Killing vectors of Robertson-Walker spacetimes. For the last case in - kR = 0, k =I 0 we provide an outline of the integration process. This case gives conformal Killing vectors which do not reduce to those of RobertsonWalker spacetimes. A number of the calculations performed in finding the solution of the conformal Killing vector equation are extremely difficult to analyse by hand. We therefore utilise the symbolic manipulation capabilities of Mathematica (Ver 2.0) (Wolfram 1991) to assist with calculations

Developing a human capital scorecard for lean implementation within an engineering environment : the case of Transnet Coach business unit

Research report presented to SBL, Unisa, Midrand.Lean manufacturing is a very good and effective concept of managing a company. The philosophy of reducing wastes found in a manufacturing business is a sound idea. When these wastes are minimized, the quality of the products or services is improved, the production time and the cost of manufacturing the goods is reduced. With this in mind, many companies go through lean manufacturing training to get the most out of their systems. But this is only achieved if there is a proper implementation lean manufacturing plan. However, despite the training and plans, some companies have trouble in implementing lean manufacturing systems. There are different reasons in the failure of implementing lean manufacturing principles in projects. One of them is the difficulty in grasping the true nature of lean manufacturing from a human capital perspective.Graduate School of Business LeadershipM. B. L

Lie symmetries for equations in conformal geometries

We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been found in practice. We use the method of Lie analysis of differential equations to obtain new group invariant solutions to conformally related Petrov type D spacetimes. Four cases arise depending on the nature of the Lie symmetry generator. In three cases we are in a position to solve the master field equation in terms of elementary functions. In the fourth case special solutions in terms of Bessel functions are obtained. These solutions contain known models as special cases.Comment: 19 pages, To appear in J. Phys.

Spherical conformal models for compact stars

Abstract We consider spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. The conformal symmetry condition generates an integral relationship between the gravitational potentials. We solve this condition to find a new anisotropic solution to the Einstein field equations. We demonstrate that the exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass–radius limit and the surface red shift are consistent with observational constraints

2 -O-Alkyl Derivatives and 5 -Analogues of 5-Aminoimidazole-4-carboxamide-1-beta-D-ribofuranoside (AICAR) as Potential Hsp90 Inhibitors

Some selective preparations of AICAR-related compounds modified at the 2- or 5-position of the ribose moiety are reported herein. In particular, 5-azido, 5-amino, 5-O-benzyl and a series of 2-O-alkylated AICAR derivatives have been synthesized. These compounds were derived from appropriately functionalized inosines by opening the pyrimidine ring at the hypoxanthine residue. The target derivatives were designed with the purpose of studying the effect of AICAR structural modifications on its ability to inhibit Hsp90, one of the biological targets for the development of anticancer agents. Nevertheless, the development of AICAR-like compounds is an appealing objective also because of their potential therapeutic application in the field of metabolic studies