Generic Spherically Symmetric Thin-shells in General Relativity

We give a full investigation and assessment on the general spherically symmetric time-like thin shells in general relativity. In this main stream, we give the details of the Israel junction conditions which are used for gluing two distinct space-times on a hyper-surfaces including the case of time-like shells. We also study the general stability of thin-shells against a radial perturbation. Our results are fully analytic in closed forms. Keywords: Thin-shells, General relativity, Spherically symmetric, Stability, Israel junction conditions.