Static solutions for brane models with a bulk scalar field

We present static solutions of the 5-dimensional Einstein equations in the brane-world scenario by using two different approaches for the stabilizatio n of the extra dimension. Assuming a "phenomenological" stabilization mecha nism, that creates a non-vanishing (T) over cap(5)(5) in the bulk, we const ruct a two-brane model, which allows both branes to have positive self-ener gies. We then consider a candidate theory for the dynamical stabilization, through the introduction of a massless scalar field in the bulk, which inte racts with the branes. We find exact static solutions for the metric and sc alar field in the bulk and demonstrate that the inter-brane distance is det ermined by the parameters of scalar field-brane interactions. However, thes e solutions are always accompanied by a correlation between the bulk cosmol ogical constant, the brane self-energies and the interaction terms of the s calar field with the branes and thus cannot be considered as candidates for the phenomenologically viable stabilized geometry. We find that the aforem entioned correlation cannot be avoided even in the case of a single-brane s olution with positive self-energy where the fifth dimension ends on a singu larity. (C) 2000 Elsevier Science B.V. All rights reserved.