2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184212The Casimir effect due to conformally coupled bulk scalar fields on background of conformally flat brane-world geometries is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy-momentum tensor and vacuum forces acting on boundaries. The special case of the AdS bulk is considered and the application to the Randall-Sundrum scenario is discussed. The possibility for the radion stabilization by the vacuum forces is demonstrated.10 pages, 4 figures, references added, accepted for publication in Phys. Lett. BHigh Energy Physics - Theorytext