Spherically Symmetric solutions on a cosmological dynamical background with BSSN equations

International audienceWe give a summary of the work presented in [1]. We expose a numerical method for the study of cosmological problems in spherical symmetry in full General Relativity. The stability of the code close to the origin is made possible through the use of the Partially Implicit Runge-Kutta (PIRK) algorithm described in [2]. We demonstrate the stability and convergence properties and give a simple application to the evolution of the Lemaître-Tolman-Bondi spacetime. This work is a generalisation of the study given in [3] performed on an asymptotically flat background