Second Randall-Sundrum brane world scenario with a nonminimally coupled bulk scalar field

In our previous work of [K. Farakos and P. Pasipoularides, Phys. Lett. B 621, 224 (2005).] we studied the stability of the RS2 model with a nonminimally coupled bulk scalar field $\ensuremath{\phi}$, and we found that in appropriate regions of $\ensuremath{\xi}$ the standard RS2 vacuum becomes unstable. The question that arises is whether there exists other new static stable solutions where the system can relax. In this work, by solving numerically the Einstein equations with the appropriate boundary conditions on the brane, we find that depending on the value of the nonminimal coupling $\ensuremath{\xi}$, this model possesses three classes of new static solutions with different characteristics. We also examine what happens when the fine-tuning of the RS2 model is violated, and we obtain that these three classes of solutions are preserved in appropriate regions of the parameter space of the problem. The stability properties and possible physical implications of these new solutions are discussed in the main part of this paper. Especially in the case where $\ensuremath{\xi}={\ensuremath{\xi}}_{c}$ (${\ensuremath{\xi}}_{c}$ is the five-dimensional conformal coupling) and the fine-tuning is violated, we obtain a physically interesting static stable solution.