Bouncing cosmological solutions due to the self-gravitational corrections and their stability

In this paper we consider the bouncing braneworld scenario, in which the bulk is given by a five-dimensional AdS black hole spacetime with matter field confined in a $D_3$ brane. Exploiting the CFT/FRW-cosmology relation, we consider the self-gravitational corrections to the first Friedmann-like equation which is the equation of the brane motion. The self-gravitational corrections act as a source of stiff matter contrary to standard FRW cosmology where the charge of the black hole plays this role. Then, we study the stability of solutions with respect to homogeneous and isotropic perturbations. Specifically, if we do not consider the self-gravitational corrections, the AdS black hole with zero ADM mass, and open horizon is an attractor, while, if we consider the self-gravitational corrections, the AdS black hole with zero ADM mass and flat horizon, is a repeller