STUDIES ON SCATTERING AND QUASI-NORMAL MODES IN BLACK HOLE SPACE-TIMES

The question of stability of black hole was first studied by Regge and Wheeler who investigated linear perturbations of the exterior Schwarzschild spacetime. Further work on this problem led to the study of quasi-normal modes which is believed as a characteristic sound of black holes. Quasi-normal modes (QNMs) describe the damped oscillations under perturbations in the surrounding geometry of a black hole with frequencies and damping times of oscillations entirely fixed by the black hole parameters.In the present work we study the influence of cosmic string on the QNMs of various black hole background spacetimes which are perturbed by a massless Dirac field.

Fast imaging of laser-blow-off plume:Lateral confinement in ambient environment

The dynamics of plasma plume, formed by the laser-blow-off of multicomponent LiF-C thin film under various ambient pressures ranging from high vacuum to argon pressure of 3 Torr, has been studied using fast imaging technique. In vacuum, the plume has ellipsoidal shape. With the increase in the ambient pressure, sharp plume boundary is developed showing a focusing-like confinement in the lateral space behavior in the front end, which persists for long times. At higher ambient pressure (> 10−1 Torr ), structures are developed in the plasma plume due to hydrodynamic instability/turbulences.

Synthesis and crystal structure of cobalt(III) complex with a Schiff base and azide

The cobalt(III) complex, [Co(L)2(N3)2]2(ClO4)2, L being a Schiff base N-[phenyl(pyridin-2-yl)methylene]aniline has been synthesized and the crystal structure determined using X-ray crystallography. The complex crystallizes in triclinic system, space group P-1 with unit cell parameters a=10.9367(9) , b=18.0817(17) , c=20.1629(16) , α=111.341(2), β=91.622(2), γ=107.5030(10), V=3499.1(5) 3 and Z=2. It crystallizes with two independent molecules in the asymmetric unit. The two cobalt atoms are hexa-coordinate and have a distorted octahedral geometry, satisfied by four nitrogen atoms from two molecules of the Schiff base and two nitrogen atoms from the monodentate azide group. The perchlorate ions are non-coordinating.

Theory of differential inequalities with appliciations to singular perturbiation problems and method of lines

During recent years, the theory of differential inequalities has been extensively used to discuss singular perturbation problems and method of lines to partial differential equations. The present thesis deals with some differential inequality theorems and their applications to singularly perturbed initial value problems, boundary value problems for ordinary differential equations in Banach space and initial boundary value problems for parabolic differential equations. The method of lines to parabolic and elliptic differential equations are also dealt The thesis is organised into nine chapters

Versatile binding properties of a di-2-pyridyl ketone nicotinoylhydrazone ligand: Crystal structure of a Cu(II) complex

Six new copper complexes of di-2-pyridyl ketone nicotinoylhydrazone (HDKN) have been synthesized. The complexes have been characterized by a variety of spectroscopic techniques and the structure of [Cu(DKN)2]·H2O has been determined by single crystal X-ray diffraction. The compound [Cu(DKN)2]·H2O crystallized in the monoclinic space group P21 and has a distorted octahedral geometry. The IR spectra revealed the presence of variable modes of chelation for the investigated ligand. The EPR spectra of compounds [Cu2(DKN)2( -N3)2] and [Cu2(DKN)2( -NCS)2] in polycrystalline state suggest a dimeric structure as they exhibited a half field signal, which indicate the presence of a weak interaction between two Cu(II) ions in these complexes

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.