Exact Solutions in Gravity: A journey through spacetime with the Kerr-Schild ansatz

The Kerr-Schild metric ansatz can be expressed in the form g_{ab} = \gbar_{ab}+\lambda k_ak_b, where \gbar_{ab} is a background metric satisfying Einstein\u27s equations, $k_a$ is a null-vector, and $\lambda$ is a free parameter. It was discovered in 1963 while searching for the elusive rotating black hole solutions to Einstein\u27s equations, fifty years after the static solution was found and Einstein first formulated his theory of general relativity. While the ansatz has proved an excellent tool in the search for new exact solutions since then, its scope is limited, particularly with respect to higher dimensional theories. In this thesis, we present the analysis behind three possible modifications. In the first case a spacelike vector is added to the ansatz, and we show that many, although not all, of the simplifications that occur in the Kerr-Schild case continue to hold for the extended version of the ansatz. In the second case we look at the Kerr-Schild ansatz in the context of higher curvature theories of gravity; specifically Lovelock gravity which organizes terms in the Lagrangian in such a way that the theory is ghost-free and the equations of motion remain second order. We find that the field equations reduce, in a similar manner as in the Kerr-Schild case, to a single equation of order $\lambda^p$ for unique vacuum theories of order $p$ in the curvature. Finally, we investigate the role of the Kerr-Schild ansatz in the context of Kaluza-Klein gravity theories

Sum Rule for the ADM Mass and Tensions in Planar AdS Spacetimes

An asymptotically planar AdS spacetimes is characterized by its ADM mass and tensions. We define an additional ADM charge Q associated with the scaling Killing vector of AdS, show that Q is given by a certain sum over the ADM mass and tensions and that Q vanishes on solutions to the Einstein equation with negative cosmological constant. The sum rule for the mass and tensions thus established corresponds in an AdS/CFT context to the vanishing of the trace of the boundary stress tensor. We also show that an analogous sum rule holds for local planar sources of stress-energy sources in AdS. In a simple model consisting of a static, plane symmetric source we find that the perturbative stress-energy tensor must be tracefree.Comment: 15 pages; v2 minor change

An extended Kerr–Schild ansatz

We present an analysis of the vacuum Einstein equations for a recently proposed extension of the Kerr–Schild ansatz that includes a spacelike vector field as well as the usual Kerr–Schild null vector. We show that many, although not all, of the simplifications that occur in the Kerr–Schild case continue to hold for the extended ansatz. In particular, we find a simple set of sufficient conditions on the vectors such that the vacuum field equations truncate beyond quadratic order in an expansion around a general vacuum background solution. We extend our analysis to the electrovac case with a related ansatz for the gauge field

Gravitational Tension and Thermodynamics of Planar AdS Spacetimes

We derive new thermodynamic relations for asymptotically planar AdS black hole and soliton solutions. In addition to the ADM mass, these spacetimes are characterized by gravitational tensions in each of the planar spatial directions. We show that with planar AdS asymptotics, the sum of the ADM mass and tensions necessarily vanishes, as one would expect from the AdS /CFT correspondence. Each Killing vector of such a spacetime leads to a Smarr formula relating the ADM mass and tensions, the black hole horizon and soliton bubble areas, and a set of thermodynamic volumes that arise due to the non-vanishing cosmological constant. These Smarr relations display an interesting symmetry between black holes and bubbles, being invariant under the simultaneous interchange of the mass and black hole horizon area with the tension and soliton bubble area. This property may indicate a symmetry between the confining and deconfined phases of the dual gauge theory.Comment: 23 pages; v2 references adde

Counselling at the Workplace in Tanzania What can Distance Education do?

his paper examines practice in counselling at workplaces. It draws examples from Tanzania. Authors define counselling as a collaborative approach towards problem solving. It is a step-by-step process of self-actualization guided by a counsellor. The authors are of the view that in most workplaces in Tanzania, for instance, there is a vacuum in counselling activities. Workers have very few professional counsellors to go to for guidance and counselling. This vacuum is usually promptly filled up with managerial actions, trade unionism and personal efforts towards individualisation which is merely advice and not counselling. They further argue that, both trade unionists and managers have objectives sometimes different from those of workers. In other instances, they frustrate the workers instead of helping them to fruitful and well-informed decisions. The paper concludes that the vacuum that exists in counselling at the workplace may be damaging to some work relations, institutional services, and can be a source of job dissatisfaction and low productivity. Thus it must be replaced with professional counselling services. The paper further argues that even where professional counsellors are employed (for example educational institutions like universities), only students are counselled and the workers are not covered as if they have no problems. Counsellors have strictly prescribed duties of dealing with students only. This paper recommends that distance education can be used in various forms to train counsellors for workplaces. Both short and long term programmes meant to gloom counsellors capable of professionally guiding and counselling workers can be developed.Keywords: Counselling at the workplace, distance education, trade unionism, individuation, managerial action

Kerr-Schild spacetimes with (A)dS background

General properties of Kerr-Schild spacetimes with (A)dS background in arbitrary dimension are studied. It is shown that the geodetic Kerr-Schild vector k is a multiple WAND of the spacetime. Einstein Kerr-Schild spacetimes with non-expanding k are shown to be of Weyl type N, while the expanding spacetimes are of type II or D. It is shown that this class of spacetimes obeys the optical constraint. This allows us to solve Sachs equation, determine r-dependence of boost weight zero components of the Weyl tensor and discuss curvature singularities.Comment: 17 pages, minor change

An analysis of Brazilian sugarcane bagasse ash behavior under thermal gasification.

Background: Ashes from sugarcane were analyzed by X-ray fluorescence, ash content, X-ray diffraction, scanning electron microscopy (SEM), and energy dispersive spectroscopy (EDS). FactSage 6.4 database software was used to estimate viscosity at high temperatures (900 - 1550°C) of them. Results: The results showed that although ashes from sugarcane bagasse contain silica, most of its SiO2 is from soil contamination. Higher and lower silica samples treated at 1350°C for 20 minutes showed that the fine portion of fraction of the ashes melted at this temperature. Conclusions: The melting phase could act as sticking flux for the coarse silica particles on the gasifier bottom wall, which could compromise the gasification process

Environmental screening tools for assessment of infrastructure plans based on biodiversity preservation and global warming (PEIT, Spain).

Most Strategic Environmental Assessment (SEA) research has been concerned with SEA as a procedure, and there have been relatively few developments and tests of analytical methodologies. The first stage of the SEA is the ‘screening’, which is the process whereby a decision is taken on whether or not SEA is required for a particular programme or plan. The effectiveness of screening and SEA procedures will depend on how well the assessment fits into the planning from the early stages of the decision-making process. However, it is difficult to prepare the environmental screening for an infrastructure plan involving a whole country. To be useful, such methodologies must be fast and simple. We have developed two screening tools which would make it possible to estimate promptly the overall impact an infrastructure plan might have on biodiversity and global warming for a whole country, in order to generate planning alternatives, and to determine whether or not SEA is required for a particular infrastructure plan