Stability analysis of 5D gravitational solutions with N bulk scalar fields

We study the stability of 5D gravitational solutions containing an arbitrary number of scalar fields. A closed set of equations is derived which governs the background and perturbations of N scalar fields and the metric, for arbitrary bulk and boundary scalar potentials. In particular the effect of the energy-momentum tensor of the scalar fields on the geometry is fully taken into account, together with all the perturbations of the system. The equations are explicitly written as an eigenvalue problem, which can be readily solved to determine the stability of the system and obtain the properties of the fluctuations, such as masses and couplings. As an example, we study a dynamical soft-wall model with two bulk scalar fields used to model the hadron spectrum of QCD and the Higgs sector of electroweak physics. It is shown that there are no tachyonic modes, and that there is a (radion) mode whose mass is suppressed by a large logarithm compared to that of the other Kaluza-Klein modes.