Generic junction conditions in brane-world scenarios

We present the generic junction conditions obeyed by a co-dimension one brane in an arbitrary background space–time. As well as the usual Darmois–Israel junction conditions which relate the discontinuity in the extrinsic curvature to the energy–momentum tensor of matter which is localized to the brane, we point out that another condition must also be obeyed. This condition, which is the analogous to Newtonʹs second law for a point particle, is trivially satisfied when Z2 symmetry is enforced by hand, but in more general circumstances governs the evolution of the brane world-volume. As an illustration of its effect we compute the force on the brane due to a form field.