STABILITY ANALYSIS OF SELF-GRAVITATING COLLAPSING SYSTEMS

Abstract

This thesis deals with the dynamical instability as well as inhomogeneities in self- gravitating collapsing objects. For this purpose, the matter distribution is considered imperfect due to anisotropic pressure, shear and bulk viscosity, dissipation in di®usion and streaming out limits and electromagnetic e®ects. For instability regimes, the interior region is taken as spherical, cylindrical and axially symmetric spacetimes which are matched with suitable exterior to explore Darmois conditions. The ¯eld equations and conservation laws are formulated and then perturbed up to ¯rst order in perturbation parameter to construct the collapse equation. The instability regimes are investigated under both N and pN approximations. A crucial role of adiabatic index has been analyzed in the presence of expansion scalar. For spherical con¯guration, the matter distribution is considered to be charged anisotropic dissipative with shear viscosity. The charged cylindrical geometry is dis- cussed with three types of °uid con¯gurations. In the ¯rst case, we take anisotropic pressure, bulk viscosity and dissipation only in di®usion approximation. The second case studies the instability epochs with anisotropic pressure under zero expansion con- dition while in the third case we take isotropic °uid with dissipation in streaming out limit. The dynamical instability for axially symmetric geometry includes two kinds of matter con¯gurations. Initially, this analysis is done only with anisotropic matter, but later we discuss the role of heat °ux and shear viscosity as well. We conclude that the radial pro¯le of material variables like energy density, principal stresses, dissipation, viscosity and electric charge control the stability of self-gravitating objects. The inhomogeneity factors have been identi¯ed for charged plane symmetric space- time with some particular cases of non-dissipative and dissipative °uids. In the non- dissipative case, we analyze inhomogeneity factor for dust, isotropic and anisotropic matter distributions while dissipative matter distribution includes only geodesic dust °uid. We ¯nd that electric charge increases inhomogeneity in the energy density, which is due to shear scalar, anisotropy and dissipation. Also, we explore some dynamical variables, structure scalars as well as an explicit expression for the super- Poynting vector associated with tilted and non-tilted Szekeres spacetime.