Stability of Spherically Symmetric Timelike Thin-shells in General Relativity

In this thesis we study spherically symmetric timelike thin-shells in 3+1-dimensional bulk spacetime. We first introduce the cut and paste formalism which is used to make thin-shells in general relativity and then we investigate the stability of such thinshells. Basically, in 3+1-dimensional bulk spacetime a timelike thin-shell is a 2+1- dimensional hyperplane whose normal 4-vector is a spacelike vector at any point on the hyperplane. A thin-shell connects two different parts of the bulk, therefore it has to satisfy some conditions which are called the Israel-junction conditions. In accordance with these conditions, the first fundamental form of the thin-shell must be continuous while its second fundamental form is not and it requires energymomentum tensor on the thin-shell. Keywords: General relativity; Thin-shell; Timelike hypersurface; Stability; Linear perturbation;