Radion stability and induced, on-brane geometries in an effective scalar-tensor theory of gravity

About a decade ago, using a specific expansion scheme, effective, on-brane scalar tensor theories of gravity were proposed by Kanno and Soda (Phys.Rev. {\bf D 66} 083506 ,(2002)) in the context of the warped two brane model of Randall--Sundrum. The inter-related effective theories on both the branes were derived with the space-time dependent radion field playing a crucial role. Taking a re-look at this effective theory, we find cosmological and spherically symmetric, static solutions sourced by a radion--induced, effective stress energy, as well as additional, on-brane matter. The distance between the branes (governed by the time or space dependent radion) is shown to be stable and asymptotically non-zero, thereby setting aside any possibility of brane collisions. It turns out that the inclusion of on-brane matter plays a decisive role in stabilising the radion - a fact which we demonstrate through our solutions.