Inhomogeneous Dark Radiation Dynamics on a de Sitter Brane

Assuming spherical symmetry we analyse the dynamics of an inhomogeneous dark radiation vaccum on a Randall and Sundrum 3-brane world. Under certain natural conditions we show that the effective Einstein equations on the brane form a closed system. On a de Sitter brane and for negative dark energy density we determine exact dynamical and inhomogeneous solutions which depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial configuration. We also identify the conditions leading to the formation of a singularity or of regular bounces inside the dark radiation vaccum.