Physical Viability and Stability of Self-gravitating Systems

Abstract

The main purpose of this thesis is to study various astrophysical and cosmological aspects in the background of general relativity. Firstly, we discuss the extended geometric deformation decoupling technique to derive new exact anisotropic solutions for static self-gravitating systems in the absence as well as presence of electromagnetic field. We consider two isotropic Tolman IV (uncharged model) and Krori-Barua solutions (charged model) and extend them to anisotropic domains by transforming both temporal as well as radial metric potentials. The physical viability and stability of interior anisotropic solutions are examined through graphical analysis of energy bounds, causality conditions and adiabatic index for different star candidates. Secondly, we investigate the impact of anisotropy on dynamical instability of non static cylindrical configuration and also inspect the stability of FRW universe model through phase space analysis in the presence of nonlinear electrodynamics. We use Eulerian and Lagrangian approaches to establish a linearized perturbed form of dy namical equations. The conservation of baryon number is applied to evaluate per turbed radial pressure in terms of an adiabatic index. A variational principle is used to find characteristic frequency which helps to compute the instability criteria of gaseous star. For the study of anisotropic and homogeneous universe, we introduce normal ized dimensionless quantities to construct an autonomous system of equations. The critical points and respective eigenvalues are evaluated for different model parameters to analyze the stability of the cosmos. Finally, we formulate the analytic expressions of the effective potential and grey body factor for the uncharged as well as charged rotating black holes in the presence of the quintessential field. To analyze the profile of effective potential, we transform the radial equation of motion into standard Schr¨odinger form through tortoise coor dinate. The two asymptotic solutions, in the form of hypergeometric functions, are xiixiii computed at distinct radial regions such as a black hole and cosmological horizons determined by the quintessence. To extend the viability over the whole radial regime, we match the analytical solutions smoothly in an intermediate region by using a semi classical approach. We also calculate the emission rates and absorption cross-section for the massless scalar fields to elaborate on the significance of our result.