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.

A Study of Some Centrality Measures in Graphs

Centrality is in fact one of the fundamental notions in graph theory which has established its close connection with various other areas like Social networks, Flow networks, Facility location problems etc. Even though a plethora of centrality measures have been introduced from time to time, according to the changing demands, the term is not well defined and we can only give some common qualities that a centrality measure is expected to have. Nodes with high centrality scores are often more likely to be very powerful, indispensable, influential, easy propagators of information, significant in maintaining the cohesion of the group and are easily susceptible to anything that disseminate in the network.

Investigations on the structural, optical and magnetic properties of nanostructured cerium oxide in pure and doped forms and its polymer nanocomposites

In recent years, nanoscience and nanotechnology has emerged as one of the most important and exciting frontier areas of research interest in almost all fields of science and technology. This technology provides the path of many breakthrough changes in the near future in many areas of advanced technological applications. Nanotechnology is an interdisciplinary area of research and development. The advent of nanotechnology in the modern times and the beginning of its systematic study can be thought of to have begun with a lecture by the famous physicist Richard Feynman. In 1960 he presented a visionary and prophetic lecture at the meeting of the American Physical Society entitled “there is plenty of room at the bottom” where he speculated on the possibility and potential of nanosized materials. Synthesis of nanomaterials and nanostructures are the essential aspects of nanotechnology. Studies on new physical properties and applications of nanomaterials are possible only when materials are made available with desired size, morphology, crystal structure and chemical composition. Cerium oxide (ceria) is one of the important functional materials with high mechanical strength, thermal stability, excellent optical properties, appreciable oxygen ion conductivity and oxygen storage capacity. Ceria finds a variety of applications in mechanical polishing of microelectronic devices, as catalysts for three-way automatic exhaust systems and as additives in ceramics and phosphors. The doped ceria usually has enhanced catalytic and electrical properties, which depend on a series of factors such as the particle size, the structural characteristics, morphology etc. Ceria based solid solutions have been widely identified as promising electrolytes for intermediate temperature solid oxide fuel cells (SOFC). The success of many promising device technologies depends on the suitable powder synthesis techniques. The challenge for introducing new nanopowder synthesis techniques is to preserve high material quality while attaining the desired composition. The method adopted should give reproducible powder properties, high yield and must be time and energy effective. The use of a variety of new materials in many technological applications has been realized through the use of thin films of these materials. Thus the development of any new material will have good application potential if it can be deposited in thin film form with the same properties. The advantageous properties of thin films include the possibility of tailoring the properties according to film thickness, small mass of the materials involved and high surface to volume ratio. The synthesis of polymer nanocomposites is an integral aspect of polymer nanotechnology. By inserting the nanometric inorganic compounds, the properties of polymers can be improved and this has a lot of applications depending upon the inorganic filler material present in the polymer.