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.

Barriers Faced By Micro, Small And Medium Enterprises In Raising Finance

Worldwide, Micro, Small and Medium Enterprises (MSMEs) have been accepted as an engine of economic growth and for promoting equitable development. In developing countries including India, Micro, Small and Medium Enterprises sector constitute an important part in its development. In spite of this importance, this sector face number of constraints like absence of adequate and timely supply of bank finance, difficulties in procuring raw materials, marketing and distribution challenges and non availability of suitable technology. Review of literature found that there exists problem in accessing finance from banks and financial institutions and this problem may differ from region to region, between sectors, or between individual enterprises within a sector. This paper tries to identify the various barriers faced by these units in raising finance and also try to identify the various sources of finance other than banks. The study is based upon the primary data collected from the 200 MSMEs owners in Kozhikode District of Kerala. The data has been analysed with the help of percentage. The study attempts to submit some recommendations to enhance the overall credit accessibility to MSMEs sector

Geophysical Constraints on Structure and Tectonics of the Eastern Arabian Sea and the Adjoining West Coast of India with Special Reference to the Kerala Basin

The main objective of the present study is to model the gravity fields in terms of lithospheric structure below the western continental margin of India (WCMI) identify zones of crustal mass anomalies and attempt to infer the location of Ocean Continent transition in the Arabian Sea. In this study, the area starting from the western shield margin to the region covering the deep oceanic parts of the Arabian Sea which is bounded by Carlsberg and Cerg and Central Indian ridges in the south, eastern part of the Indus Cone in the west and falling between 630E and 800E longitudes, and 50N - 240N latitudes has been considered. The vast amount of seismic reflection and refraction data in the form of crustal velocities, basement configuration and crustal thicknesses available for the west coast as well as the eastern Arabian Sea has been utilized for this purpose

Dynamics of the logistic map under discrete parametric perturbation

By introducing a periodic perturbation in the control parameter of the logistic map we have investigated the period locking properties of the map. The map then gets locked onto the periodicity of the perturbation for a wide range of values of the parameter and hence can lead to a control of the chaotic regime. This parametrically perturbed map exhibits many other interesting features like the presence of bubble structures, repeated reappearance of periodic cycles beyond the chaotic regime, dependence of the escape parameter on the seed value and also on the initial phase of the perturbation etc.