Studies on scattering and thermodynamics of black holes in f(R) theory and Einstein's theory

One of the interesting consequences of Einstein's General Theory of Relativity is the black hole solutions. Until the observation made by Hawking in 1970s, it was believed that black holes are perfectly black. The General Theory of Relativity says that black holes are objects which absorb both matter and radiation crossing the event horizon. The event horizon is a surface through which even light is not able to escape. It acts as a one sided membrane that allows the passage of particles only in one direction i.e. towards the center of black holes. All the particles that are absorbed by black hole increases the mass of the black hole and thus the size of event horizon also increases. Hawking showed in 1970s that when applying quantum mechanical laws to black holes they are not perfectly black but they can emit radiation. Thus the black hole can have temperature known as Hawking temperature. In the thesis we have studied some aspects of black holes in f(R) theory of gravity and Einstein's General Theory of Relativity. The scattering of scalar field in this background space time studied in the first chapter shows that the extended black hole will scatter scalar waves and have a scattering cross section and applying tunneling mechanism we have obtained the Hawking temperature of this black hole. In the following chapter we have investigated the quasinormal properties of the extended black hole. We have studied the electromagnetic and scalar perturbations in this space-time and find that the black hole frequencies are complex and show exponential damping indicating the black hole is stable against the perturbations. In the present study we show that not only the black holes exist in modified gravities but also they have similar properties of black hole space times in General Theory of Relativity. 2 + 1 black holes or three dimensional black holes are simplified examples of more complicated four dimensional black holes. Thus these models of black holes are known as toy models of black holes in four dimensional black holes in General theory of Relativity. We have studied some properties of these types of black holes in Einstein model (General Theory of Relativity). A three dimensional black hole known as MSW is taken for our study. The thermodynamics and spectroscopy of MSW black hole are studied and obtained the area spectrum which is equispaced and different thermo dynamical properties are studied. The Dirac perturbation of this three dimensional black hole is studied and the resulting quasinormal spectrum of this three dimensional black hole is obtained. The different quasinormal frequencies are tabulated in tables and these values show an exponential damping of oscillations indicating the black hole is stable against the mass less Dirac perturbation. In General Theory of Relativity almost all solutions contain singularities. The cosmological solution and different black hole solutions of Einstein's field equation contain singularities. The regular black hole solutions are those which are solutions of Einstein's equation and have no singularity at the origin. These solutions possess event horizon but have no central singularity. Such a solution was first put forward by Bardeen. Hayward proposed a similar regular black hole solution. We have studied the thermodynamics and spectroscopy of Hay-ward regular black holes. We have also obtained the different thermodynamic properties and the area spectrum. The area spectrum is a function of the horizon radius. The entropy-heat capacity curve has a discontinuity at some value of entropy showing a phase transition.

The Quadric Reference Surface: Theory and Applications

The conceptual component of this work is about "reference surfaces'' which are the dual of reference frames often used for shape representation purposes. The theoretical component of this work involves the question of whether one can find a unique (and simple) mapping that aligns two arbitrary perspective views of an opaque textured quadric surface in 3D, given (i) few corresponding points in the two views, or (ii) the outline conic of the surface in one view (only) and few corresponding points in the two views. The practical component of this work is concerned with applying the theoretical results as tools for the task of achieving full correspondence between views of arbitrary objects.

Conditional compositional biplots: theory and application

The biplot has proved to be a powerful descriptive and analytical tool in many areas of applications of statistics. For compositional data the necessary theoretical adaptation has been provided, with illustrative applications, by Aitchison (1990) and Aitchison and Greenacre (2002). These papers were restricted to the interpretation of simple compositional data sets. In many situations the problem has to be described in some form of conditional modelling. For example, in a clinical trial where interest is in how patients’ steroid metabolite compositions may change as a result of different treatment regimes, interest is in relating the compositions after treatment to the compositions before treatment and the nature of the treatments applied. To study this through a biplot technique requires the development of some form of conditional compositional biplot. This is the purpose of this paper. We choose as a motivating application an analysis of the 1992 US President ial Election, where interest may be in how the three-part composition, the percentage division among the three candidates - Bush, Clinton and Perot - of the presidential vote in each state, depends on the ethnic composition and on the urban-rural composition of the state. The methodology of conditional compositional biplots is first developed and a detailed interpretation of the 1992 US Presidential Election provided. We use a second application involving the conditional variability of tektite mineral compositions with respect to major oxide compositions to demonstrate some hazards of simplistic interpretation of biplots. Finally we conjecture on further possible applications of conditional compositional biplots

TU Graz: Course: 707.000 Web Science and Web Technology: Lecture 3: Network Theory and Terminology

In this class, we will discuss network theory fundamentals, including concepts such as diameter, distance, clustering coefficient and others. We will also discuss different types of networks, such as scale-free networks, random networks etc. Readings: Graph structure in the Web, A. Broder and R. Kumar and F. Maghoul and P. Raghavan and S. Rajagopalan and R. Stata and A. Tomkins and J. Wiener Computer Networks 33 309--320 (2000) [Web link, Alternative Link] Optional: The Structure and Function of Complex Networks, M.E.J. Newman, SIAM Review 45 167--256 (2003) [Web link] Original course at: http://kmi.tugraz.at/staff/markus/courses/SS2008/707.000_web-science/

Graph Theory and Social Networks Tutorial

For COMP60

Game Theory and Addiction

A brief one lecture introduction to Game Theory and Addiction techniques for building a games.

Alternatives to Reparations in International Investment Arbitration– A Debate Between Theory and Practice

An analysis of the alternatives of compensation in relation to international investment disputes is relevant, because a pecuniary award is not always the appropriate remedy to solve disputes arising between investors and States. This is the case because States may be increasingly interested in opting for a different type of compensation. Furthermore, it is still not clear whether arbitral tribunals have recognised alternative types of awarding damages in respect of international investments disputes. This analysis comprises two principal components, the first, is to identify whether or not the tribunals may render an award that not only demands the payment of a sum of money but also considers some other means of compensation. The second, centres on how compliance with these non-pecuniary awards may be demanded. Our approach to these two principal components will always revolve around the idea of respecting the sovereignty of the State, bearing in mind that the execution of an arbitral award, which obliges the State to refrain from or to perform an act in its territory, relies precisely on the sovereignty of the State to execute it. 

Teoría y práctica de la Prehistoria : perspectivas desde los extremos de Europa = Theory and practice of Prehistory : views from the edges of Europe.

Esta obra es producto de la primera, y única, Reunión Hispano-Soviética de Prehistoriadores organizada por el Departamento de Prehistoria del Centro de Estudios Históricos en el marco del convenio entre la Academia de Ciencias de la U.R.S.S. y el C.S.I.C. español. Su objetivo es promover contactos entre investigadores de ambos países. La publicación se divide en catorce partes: 1. Prefacio. 2. Prólogo. 3. El Centro de Estudios Históricos. 4. El Departamento de Prehistoria. 5. El Instituto de Arqueología de la Academia de Ciencias de Rusia. 6. Gonzalo Ruiz Zapatero. 7. Rauv M. Munchaez (ponencia). 8. Emiliano Aguirre Enríquez (ponencia). 9. Valery P. Alekseev (ponencia). 10. Alfonso Moure Romanillo (ponencia). 11. Jizri A. Amirjanoz (ponencia). 12. Eugenio N. Chernij (ponencia). 13. Arturo Ruiz Rodríguez (ponencia). 14. Valery I. Gulaiev.

Economic integration. an overview of basic economic theory and other related issues

Este documento presenta una visión amplia de la Teoría de Integración Económica desde el punto de vista de la teoría de unión aduanera. Se argumenta que dicha teoría carece de integración y que los recientes desarrollos en el tema no parecen resolver esta falla. A pesar de esto, se sugiere que los desarrollos teóricos surgidos a partir del trabajo seminal de Viner y posteriormente desarrollados por otros teóricos, son aún útiles como herramienta de investigación empírica en el tema.

English teaching in the secondary school : linking theory and practice.

Es un texto para la enseñanza de la lengua inglesa en las escuelas secundarias dirigido a los profesores que estudian, están recién titulados ó son experimentados docentes. Cumple con los requisitos del plan nacional de estudios inglés para el año 2000 y con la Estrategia Nacional de Alfabetización (National Literacy Strategy) para la etapa 3 (key stage 3). Entre sus objetivos están: dar ideas prácticas específicas que vinculen la teoría y la práctica y estimular el pensamiento crítico sobre la enseñanza del inglés.

Effective teaching in schools : theory and practice.

Examina los aspectos que son importantes para una enseñanza y aprendizaje eficaz en las escuelas. El recurso está dividido en tres partes que reflejan las tres tareas fundamentales de la formación docente: la primera parte se centra en ayudar a los profesores a reforzar su conocimiento y comprensión de una enseñanza eficaz y el aprendizaje del alumno; la segunda parte se centra en los aspectos individuales de buenas prácticas en el aula; desde la creación de la experiencia de aprendizaje teniendo en cuenta las diferencias pedagógicas fundamentales hasta el establecimiento de relaciones constructivas con los alumnos. La tercera parte reflexiona sobre la experiencia docente. Esta edición incluye el aprendizaje personalizado, los nuevos avances en la TIC, la enseñanza interactiva. También contiene una terminología actualizada.