Moduli fields and brane tensions: generalizing the junction conditions

Taking the Randall–Sundrum models as background scenario, we derive generalized Israel–Lanczos–Sen thin-shell junction conditions for systems in which several bulk scalar fields are non-minimally coupled to gravity. We demonstrate that the form of the junction conditions (though arguably not the physics) depends on the choice of frame. We show that generally (in any frame except the Einstein frame) the presence of a thin shell induces discontinuities in the normal derivative of the scalar field, even in the absence of any direct interaction between the thin shell and the scalar field. For some exceptional scalar field configurations the discontinuities in the derivatives of the metric and the scalar fields can feed back into each other and so persist even in the absence of any thin shell of stress-energy. PACS: 04.60.Ds, 04.62.+v, 98.80 Hw