Gravitational Perturbations of a Six Dimensional Self-Tuning Model

We investigate gravitational perturbations in a compact six-dimensional self-tuning brane model. We specifically look for analytic solutions to the perturbed Einstein equations that correspond in four-dimensions to massless or approximately massless scalars coupled to matter on the brane. The presence of such modes with gravitational couplings would be phenomenologically unacceptable. The most general solution for all such modes is obtained, but it is found that they are all eliminated by the boundary conditions. Our main result is that to linear order in perturbation theory this model does not contain any light scalars. We speculate that this model does not self-tune.