I. INTRODUCTION The possibility of extra spatial dimensions [1, 2], hidden from our current experiments and observations through compactification or warping, has opened up a wealth of options for particle physics model building [3–16] and has allowed entirely new approaches for addressing cosmological problems [17–32]. In many implementations, Standard Model (SM) fields can be confined to a submanifold, or brane, while in others they populate the entire extra- dimensional space. Common to both approaches, however, is the inclusion of bulk fields beyond pure gravity, either because they are demanded by a more complete theory, such as string theory, or because they are necessary to stabilize the extra-dimensional manifold. Thus, a complete understanding of the predictions and allowed phenomenology of extra dimension models necessarily includes a comprehensive consideration of the configurations of these bulk fields, the simplest of which are real scalars. Indeed, 4D Poincare invariance allows for these new bulk fields to acquire nontrivial static configurations along the extra dimensions. Static one-dimensional scalar configurations with a node (where the field vanishes) are known to localize wave functions of other fields near that node. In the context of extra dimensions, these kink-like scalar backgrounds can be used for example to localize bulk fermions near either boundary [33–36], allowing for interesting constructions of flavor models. They can also affect the localization of other scalar or vector fields leading to a field theoretic description of fat branes (see for example the constructions in [37–39]). Kink-like scalar configurations are a particularly interesting case to consider because the boundary conditions make it possible to obtain non-trivial general results regarding both the existence and the stability of such configurations, at least in the case of one flat extra dimension without gravity [40, 41]. In this paper we build on these previous results and extend them as far as possible to the case with a gravitating (warped) extra dimension. In the presence of gravity the kink-like configuration cannot fix and stabilize the interbrane distance [42]. It is therefore necessary to assume the existence of at least one additional stabilizing field, coupling either directly or gravitationally to the kink field. We will opt for the latter and introduce additional non-interacting scalar fields. At least one of these additional fields must be given a monotonic profile in order to stabilize the size of the extra dimension (i.e., interbrane modulus) [43]. 2