IV. KINKS IN GRAVITATING WARPED EXTRA DIMENSIONS So far we have examined static scalar field configurations in a fixed background. We have found that some of the results that were shown to hold in a flat extra-dimensional background continue to hold in a fixed warped background, and we have found useful generalizations of other results. We now want to include the dynamics of the gravitational sector and explore how these results can be extended when the gravitational backreaction is included. Therefore we now seek nontrivial static field configurations in which the warp factor has its own dynamics determined by the 5D Einstein equations. As soon as we include a dynamical gravitational sector, we are required to worry about stabilization of the extra dimension. In the above discussion we assumed that the extra dimension was stabilized and that the dynamics of the stabilization mechanism were frozen out. Here we want to include the backreaction of any matter fields on the 5D metric, and so we must include the dynamics of stabilization. A natural question to ask is whether the kink fields of interest could provide a stabilization mechanism. Unfortunately, in [42] it was shown that when one considers static solutions for both the warp factor and a single scalar field, the lightest scalar perturbative mode (the radion) will be tachyonic whenever the derivative of the scalar profile vanishes inside the interval. In other words, the system is unstable whenever the scalar field profile passes through an extremum in the bulk. This means that if we insist on obtaining a nontrivial configuration for a single scalar field with Dirichlet boundary conditions, we are guaranteed to obtain a tachyonic radion and the extra dimension will be unstable. To address this issue we will add extra scalar fields whose purpose will be to stabilize the radion as in [43]. The resulting system becomes considerably more difficult to analyze than the case with only one bulk scalar field, particularly with regard to questions about stability. On the other hand, the case with three or more scalar fields is formally no more difficult to analyze than the case with only two scalar fields. Hence we will keep our treatment general to include an arbitrary number of scalar fields χ$_{a}$ ( a, b = 1 , . . . , N ), although when we consider particular examples below, we will specialize to the case with only two scalar fields (a kink field and a non-kink field). For simplicity we will assume throughout that the scalar fields are only coupled gravitationally. 12