Codimension-two branes in six-dimensional supergravity and the cosmological constant problem

We investigate in detail recent suggestions that codimension-two braneworlds in six-dimensional supergravity might circumvent Weinberg's no-go theorem for self-tuning of the cosmological constant. The branes are given finite thickness in order to regularize mild singularities in their vicinity, and we allow them to have an arbitrary equation of state. We study perturbatively the time evolution of the solutions by solving the equations of motion linearized around a static background. Even allowing for the most general possibility of warping and nonconical singularities, the geometry does not relax to a static solution when the brane stress energies are perturbed. Rather, both the internal and external geometries become time dependent, and the system does not exhibit any self-tuning behavior.