Moduli fields and brane tensions: generalizing the junction conditions

TL;DR

This paper generalizes the junction conditions in brane-world models with multiple non-minimally coupled scalar fields, revealing how frame choice affects the physics and the behavior of scalar and metric discontinuities.

Contribution

It derives generalized junction conditions for systems with multiple scalar fields in brane-world scenarios, highlighting the impact of frame choice on these conditions.

Findings

Discontinuities in scalar field derivatives are induced by thin shells in most frames.

Frame choice influences the form of junction conditions and the resulting physics.

Scalar and metric derivatives can feedback and persist without stress-energy shells in special configurations.

Abstract

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.